Got some questions about this western islam?
Whats the facial hair situation with this western Islam do we still need beards?
Does this islam still have the culture effect where these muslims use muslim names or there own native names?
Woman's rights?
Fasting?
Sexuality etc, is it harem for fun times outside marriage and LGBT stuff, are lesbians and gay people open in society?
Western Islam is still Islam. The doctrinal difference is related not to grand-scale divergences in the framework of
sharia, but in a dispute over the correct succession of the Caliphate.
As of the Crossing, beards are considered mandatory for Muslim men. The beard is considered a mark of status and masculinity, saying nothing of its religious significance, and an entire industry exists to provide maintenance products for the beard. Some of them involve grapeseed oil; in fact, selling beard oil which includes this is one way illegal wine and brandy producers explain away the existence of their vineyards. If ever you meet a man who owns a vineyard and sells raisins and beard oil, especially if he lives in Sheresh, he's probably an illegal vintner.
Most Muslims, as you've probably seen, have adopted Arabic names at this point, but local names also slip through. It's not unusual for Andalusis, for example, to use names like Gharsiya (Garcia), Sanshu (Sancho), Bilayu (Pelagio) and other Arabized versions of Hispano-Roman names, similar to how Berbers will use Berber names like Tumart, Ziri, Tashfin and Atiyya. This is not far off how things went OTL.
Women are notable in the west - Andalusia is the "meme example," but actually West Africa is the real offender here - because of the tendency to be more lenient about
hijab than their counterparts in Arabia and Mesopotamia. Most women in the commons will wear the
khimar, but in general, the veiling tradition is weaker both here and in the Maghreb, save those areas where Zahiri and more rigorist interpretations of Maliki predominate (e.g. in Sale you can get away with a small and stylish
khimar with a nice pattern on it, while in Sijilmasa you put your life at risk if you wear one with a pattern and don't cover your face) - and that's mostly because the veiling tradition actually
predates Islam in areas where Islam originated, but has much less of a basis in Spain and the Maghreb. Religious authorities don't
condone women going around without the
khimar by any means. Women who don't wear a headscarf tend to be seen as extremely headstrong and rebellious; the likes of OTL's Wallada bint al-Mustakfi or ITTL's Majin (who often went about without a
khimar) should be taken not as the standard, but as remarkable figures. That said, while most jurists in Al-Andalus and the Maghreb will tell you to cover your head, they almost universally take the view that it is not
fard to cover the face and hands (there is, in other words, no tradition of garments like the
niqab, save in very conservative areas - indeed, it's seen as weird by most mainstream Andalusis), and the typical
khimar worn in an Andalusian city tends to be lighter and smaller than one you might see in Mecca. Covering the head is still important, but whether it extends to veiling, in other words, largely depends on how much the group in question already had a tradition of face covering.
West Africa, meanwhile, has been slow to conform to mainline Maliki jurisprudence on matters of women and
hijab. It's common for women in these societies to play outsized roles in the household and to not cover not just the head, but parts of the upper body. This is steadily changing in parts of the Sudan where contact with the Andalusians is most regular; in Tekrur and the New Cities region of Senegambia, for instance, women cover their head and bosom in the style of the Andalusians.
LGBT people are hard to place because of medieval Islam having a bit of a wobbly, contradictory relationship with the subject. While a lot of Andalusian love poetry is implicitly homoerotic and we know that there were caliphs who kept male lovers, and there's certainly evidence that homosexuality and homoeroticism were things that the elite class in Al-Andalus did, that doesn't imply the consent of God or the religious authorities - though when it's the Caliph, I guess maybe it does. A lot of poetry on the topic tends to be couched vaguely: For instance, it'll often be unclear if a love poem is addressing a woman or a man. ITTL, the situation is similar, though it's moderated a bit because the Hizamids are marginally more rigorous than the later Saqlabids and Al-Mustanjid was a marginally more active Caliph than his toothless and decadent forebears. Generally, though, the
qadi can't be everywhere or respond to everything, and gay people in Andalusia are careful either to be discreet or to be the Caliph. While your local jurist might come after you for having a same-sex lover just as he would for adultery, he's gotta know about it first. Broadly, jurists tend to hold to the position that homosexual relationships cannot ever be lawful because they are by definition not taking place within the bounds of the marriage.
Basically the gaps between
sharia and practice are explainable by what's true about all religions: The letter of the law is not always the practice of the law, and no society is perfectly rigorist or immune to a little decadence. It's why arch-rigorists and the Veiled Sanhaja tend to view Andalusians and city Berbers as decadent wretches, while the city Berbers and Andalusians tend to view the Veiled Sanhaja and arch-rigorists as pedantic Kharijites who read things into
hadith that aren't there.