Quite a long time ago, someone issued an AH challenge to have an English-speaking but Muslim population dominating North America. The OP kept moving the goalposts but in response to this, I suggested a quite wacky sequence:
1) postulate a much stronger, unified al-Andalus. It is unclear to me why the diverse, fragmented emirates and whatnot of Moorish Iberia were not capable of uniting under one strong ruling dynasty or caliph or republican federation, what have you, in the face of the existential threat to the Islamic population posed by the Reconquista which did result in an effectively unified Spanish state eventually. (Sure, there remain major regional fault lines separating the various historic kingdoms of Christian Iberia, and Portugal was only ever briefly under the Spanish crown in personal union. But from around the late 15th century into the 20th Spain was effectively unified). Perhaps OTL the demographics of conversion to Islam was limited to a small percentage of the population, and various incentives made the imported Moorish and other ruling Muslim families elitist and jealous, and this might have fed into failure for some strong single system or confederation to form? I do not know, but it hardly seems necessarily rooted in the fundamental nature of things that over many hundreds of years, such a strong dynasty, based either on an elite but large minority of converts or near total conversion of the whole population with few outliers left over would be impossible, either by benign or brutal means. Such a stronger kingdom need not occupy all of Iberia though I suppose when it reaches a tipping point that is the logical conclusion, with the Pyrenees being a logical and natural boundary where Christendom and the Muslim outpost surge sometimes over or around but generally Christians north of the range and Muslims south of it prevail and become accepted over time as the normal and even "natural" circumstance. If this "Caliphate" or grand Emirate or republican federation or whatever lasts long enough, converting enough of the Iberian population, then even going through phases of weakness or even schismatic fragmentation the zone can remain, for a later renaissance as a unified state again or with some sector of it becoming powerful and prosperous.
2) at some point, being driven in part to maritime enterprise by their isolation and opportunity (this supposes the "Emirate" as I guess I will call it has a lot of Atlantic coastline, so probably no Portugal that lasts) they become very proficient seafarers, competent to sail long distances with good navigation on the Atlantic, and come into conflict with some version or other of England. In the course of trading blows, the Emirate, perhaps with a long track record of accommodating Christian minorities under its belt in a fairly mutually agreeable way, comes to an understanding with strong Irish factions, and serving as trusted mediator and de facto High King overseas among them, organizes them into an invading army to attack England across the Irish sea, supplementing Irish bands (which are armed and otherwise equipped according to modern standards by the Emirate) with Emirate forces, the Emirate providing the bulk of the sea lift and naval cover, the still-Catholic Irish providing a high share of manpower. Because Ireland is a lot less populous than England and probably the Emirate cannot even organize the entire island to participate in this grand raid, it takes time, but the Emirate and Irish exploit factional splits among the English--perhaps England is in some ATL version of the Reformation and deeply split on sectarian lines, with the Irish having tended to break with Rome and adopt some kind of "Neo-Celtic" rite. (That's in scare quotes because I believe the lasting alleged divisions between the old first millennium sectarian split between Ireland and Rome are somewhat exaggerated, and that in reality the "Romans" absorbed a lot from the "Celtics" and the latter never really saw themselves as opposed to Rome. But now they do, rewriting history to pretty well agree with OTL moderns asserting a long and deep rift persisted). The Irish, as allies (or catspaws, depending on how one looks at it) manage over decades to get the upper hand in Great Britain (whether they go on to subdue Scotland is an optional side issue) and become hegemons of the British isles, albeit dependent on Emirate assistance, for centuries to come.
3) in this way, the subjugated English are under pressure to adopt both Gaelic and Muslim elements of culture, and being resentful of the Irish and with the Emirate the real center of power in this western outpost of Islam, prefer to Arabicize instead of Gaelicize. The Irish don't much care as long as they can stay on top and are cheerfully Arabicizing themselves, often in close parallel with English adoptions. Whether the population of the British Isles also goes Muslim, or whether it remains a hodgepodge of several Christian sects under the hegemony of Celtic Catholicism (which one presumes makes all kinds of ecumenical concessions toward harmony with their Muslim patrons, which might however fall short of even the most sycophantic Irish actually abjuring the divinity of Christ and declaring Mohammed to be the infallible and final "seal of the Prophets") with a fairly large Islamic minority of expatriate Iberians (and others from the Islamic world) and local converts, can again be an exercise for the reader--note that when I first dreamed up this sequence it was for purposes of native English speakers who were also firmly Muslim in North America, and there I emphasized the process of subjugated English speakers sticking to their mother tongue but preferring to adopt Islam over direct submission to their Irish direct overlords. That's why we have the indirect process of an Irish regime backed by an Iberian Emirate instead of the Muslim Iberians just sailing in to conquer England all by themselves, to meet a rather convoluted OP!
But I do think this can be defended as not impossible if not extremely plausible. Certainly across the substantial distance from Iberia, even a quite strongly united and comparatively wealthy and well governed version, to England, it is helpful to have a large base nearer to hand, and to recruit manpower from it. Certainly antagonism between Ireland and Great Britain has been a thing historically--not as severe as some might make it out, but it is a factor to play on, particularly if the English have just made an abortive bid for supremacy over all Ireland--something like this did happen in Irish history not long before the rise of the Tudors actually. Naturally I am having a lot of implausible fun with the idea of turning the tables of the England-Ireland relationship to be sure! So they'd need allies to prevail and make it stick, and also need to take advantage of unusual degrees of civil strife in England. But that certainly happens from time to time in English history! The idea in the old thread was to come up with a plausible source of a stream of "white" (I believe the OP stressed that, and is one reason I approached their "challenge" in a rather contrarian mood--IIRC they later moved the goalposts in a direction even more dubious) English speaking Muslim lower classes to form the grassroots of an Anglo-Arabic creole.
Here again, that North American challenge is completely by the board, we don't have to speculate on this Hiberno-English client state of a strong Iberian emirate getting a lock on North American settlement at all.
Nor do we have to suppose the Irish ascendency lasts forever; a handful of centuries ought to be enough to put a distinctively Arabic stamp on the English identity.
I do think that while initially Ireland, even somewhat united, even with the patronage of a quite rich and powerful unified Iberian emirate, prevailing against English forces in England is something of a David versus Goliath scenario and arguably ASB, they would in the middle of the last millennium have some toeholds of a sort--possibly the nature of schismatic social breakdown in England involves a recrudescence of Welsh (Cymric, that is) identity and maybe the Irish and even Emirate forces associated with them come in as allies and liberators, with Wales and perhaps an annexed or recreated Cornwall being privileged bases--then the more territory and population the Irish conquer, the stronger they get with several snowballing synergies. Back in Ireland the credibility of the originally somewhat dubious Emirate-fostered coalition of tribes is on the ascendant; population that otherwise would struggle in intertribal strife finds opportunities in subduing and holding English fiefs and thus both population pressure is somewhat drained off and intertribal relations among the stay at homes has more wiggle room for peaceful "just"settlements; a large part of exploiting conquered England would be expended on the spot in Great Britain but a portion would surely be expatriated back to Ireland subsidizing a feedback loop of rising mercantile wealth flow there that might even jump-start industry. Certainly I think if we can dare to image an Irish/Iberian alliance, based on competence in Atlantic seafaring, with the resources of England thrown into the mix exploitation of the Americas is hardly out of the question! So it might be up to a chancy and shaky start, but nearing the finish line the Gaelic High Kingdom is on firmer and firmer footing soon approaching the strength of the personal union of England and Scotland OTL eventually becoming the UK. I'd think Scotland would have to fall into the system sooner or later on some terms or other--perhaps quite attractive ones to the Scots!
One might argue, oh, even ignoring the cross-talk with Gaelic, this is a Moorish influenced England, not Arabic! I believe though the Andalusian patchwork of petty realms of OTL stressed Arabic culture as such, with of course a bit of patriotic Moorish pride as well--and just maybe perhaps, it would be a necessary condition of Islamic Iberia consolidating itself, pushing back the Reconquista and achieving this place around 1500 instead of the OTL total extinguishment by that date, for some non-Moorish, Arabic speaking faction to horn in and achieve supremacy. In that case, the most rosy scenario is that Moorish ties are indeed strong and a major element of the Emirate culture itself, but the official face the Emirate presents the world is very Arabic, and it is this identity among outsiders that the subjugated English seek to appropriate elements of, to distinguish themselves as persons worthy of consideration versus their Gaelic overlords in the eyes of the supreme Emirate patrons.
