How much of the empire are we talking about here? At a point the reformers would be the majority and manage to get through their desired reforms. Though in this case, it might mean devolving power over bishops to dukes and such. Whatever the case, it should have interesting effects with both the Dutch and Swiss.
Protestantism almost overran the Habsburg lands in the period leading up to the 30 years' war (It was one of the reasons for the Habsburg crackdown that started the war) and with a Protestant Emperor sponsoring the push Reformist beliefs should be able to reach far into society.
(on mobile right now, will post extended answer in the morning).
The idea of a non-Catholic HRE is by its very nature impossible - it violates the very ideological construct of the Empire. Firstly, before I go on, I am obliged to recommend the book "Heart of Europe" to anyone interested in learning about the HRE (and to some extent, about how medieval and early modern politics actually opetated&.
The book begins with a deconstruction of the name "Holy Romam Empire" - and his discussion of it really should be read by everyone on this board. The holy element is often underplayed in discussions about the HRE, and even medieval Europe as a whole. All too often, we try to rationalize medieval politics by distorting it to fit our modern mindset of politics - that is, our idea that economic and political factors are what drove leaders, not ideas or symbolism.
The emperors certainly didn't want to split with the pope, even during the longstanding conflicts in the high middle ages. The Empire was idealized as the protector of the mortal world, just as the pope was the protectior of the spiritual. Religion was also taken far more seriously by people than is often said; religious actions were not some political scheme to garner legitimacy. They were performed because it was their moral duty to proform them.
The biggest factor for this discussion, tho, is the Roman and imperial aspect of the title. Whereas we use the term empire rather broadly today, in the middle ages the had a very specific meaning: to be Imperial is synonymous with being Roman. This was built out of both nostalgia for Rome and out of biblical beliefs. Specifically, the biblical idea of the "4 empires" (Babalon, Assyria, Persia, Roman), and the integration of Rome into the description of the second coming. To have there be any other empire was absurd - there simply couldn't exist any new empire other than the romans.
The notion of an empire was also associated with it being universal. The HRE was built upon the idea of it being something other than the rest of Europe's kingdoms - the Empire held political superiority over all of Christiandom. That's also part of the reason you didn't see the Empire take extreme efforts to centralize- they didn't see it as something that needed to be done.
Protestants was simply incompatible with the idea that the Empire is universal, Roman, and imperial. Even if a protestant became emperor, I'd image he would have to conform to much of the catholic nature of his empire. You'd essentially have a demi-catholic, less legitimate, and likely more unpopular king of the Germans.
The point of this exercise is to see if we can find a way of changing that ideological construction in a way that justifies Protestant leadership of the Empire. The Empire can continue as the idealized protector of the world, simply joining the spiritual defense to its list of tasks. If you believe that the Pope is the Anti-christ (which the protestants largely claimed) then you need to find some way of restoring Christian control over the Empire. You can't leave the "Devil" in control of the world's defenses, either spiritually or physically.
You can still have a protestant ruler claiming a to be a universal ruler, that part of the bible was used to justify the more absolutist regimes in protestant lands later on.
The integration of Rome into the second coming came as part of the reforms associated with the early Ecumenical Councils, which a range of protestants dismiss as being against the beliefs of the early Church which they viewed as having been corrupted by Imperial involvement.
HRE believed it represented christendom. I see no reason why that wouldn't continue, as far as they believe it was the Catholics that ruined and subverted Christ's message and not them. Beside that Empire, even though it had it's fault was a general benefit to those under it, and protestant pronces would strive to keep it going, but manage it themselves.
Have the Turks be less of a threat capable of rallying support behind the habsburgs, and civil wars over rule of the empire are almost a guarantee. The greatest obstacle to overcome is that Habsburgs were in effect protecting Christendom, and that is a huge risk to undermine.
By the time Turks stopped being a threat in our world the HRE lost in its value and relugious situation was settled.
One of the protestand princes would be chosen, though I believe some Catholic electors may be kept to appease that religious group. That depends though on ferocity of fighting and clarity of victory. A fierce war that ends in Catholic forces clearly crushed might result in most if not all electors being protestant.
Brandenburg/Prussia, Saxony, Hesse might be main contenders. I doubt the title would be hereditary, princes might insist on ruler election after death of an emperor, an election with more of a bite than confirming a Habsburg as has been the case before
End result might be a more unified German world, early German unification, earlier Dutch independence and protestantism being a dominant religion in central Europe
If we are prior to or around the 1530s-1540s then the definitions of protestantism would still be fluid enough to mold in any one direction.
But we're talking about 16th and 17th Europe, not the middle ages. By the time there was even a possibility of a majority of the electors becoming Protestant, the conception of the HRE as universal was a thing of the past.
There was still a significant belief in the HRE as a universal empire to my understanding, at least for the first half of the 16th century or so, and there is no reason to drop the universal aspect of the Empire at this point. Having the Emperor claim to speak on behalf of "all true christians" would work as a powerful centralizing force across the Protestant movements. All of this really depends on the Emperor of course.
A Protestant king of the Romans would seek to issue a new Golden Bull (Reform Bull?( and have the imperial diet approve it. And he would try, if he could, to recreate the sort of theological legitimacy Catholic Emperors had through parallel structures, although there's a lot of space for maneuvre here. If he succeeds, then there's a powerful force towards cohesion and against sectarian splintering in Protestantism (and it's also going to become a very German thing, maybe appealing less to other nations).
Chances are, though, that this means an earlier 30yw...
I hadn't considered the way a Bull could be used to legitimize his reign, certainly an interesting concept. but I agree that this would definitely result in conflict much earlier on.
The OTL elections in that time period were:
1531 - Ferdinand I
1562 - Maximilian II
1575 - Rudolf II
1612 - Matthias
1619 - Ferdinand II
1636 - Ferdinand III
Which of these was closest to Habsburg losing the election to a Protestant emperor (most prominent Protestant prince probably Saxony)?
I honestly don't know, I think that Matthias and Charles in 1519 were probably the most contentious and where the Habsburgs came closest to losing (the others, had some of this as well iirc but don't have it off the top of my head).
A ever so slight problem with choosing one from their ranks (who wasn't a Habsburg) might be the crabpot nature of the German electors. The Wettins and the Hohenzollerns disliked each other (Friedrich the Wise supported Luther for political reasons, against Albrecht, archbishop of Mainz who was a Hohenzollern). The two branches of the house of Wittelsbach (Pfalz and Bavaria) weren't each other's greatest fans. And even when they DID get a Protestant king of Bohemia in the hopes of breaking the Habsburg hegemon of the imperial title, the majority still voted for a Habsburg anyway (even the Protestant king of Bohemia did, dammit! They elected him as a rival and here he was acting like a vassal). Plus, the Habsburgs ruling Hungary - the bulwark against theTurks- and Spain - sort of made them the best candidates to elect for political, if not religious reasons.
That said, a Protestant Habsburg Holy Roman Emperor might be fun. Hungary, Austria and Bohemia were reasonably Protestant until the 30YW IIRC, (Imperial line stays Catholic, Spaniah line stays Catholic, maybe a third Bohemian-Hungarian line goes Protestant-lite and they get elected king of the Germans when the imperial branch goes extinct). So my question is, why DIDN'T a branch of the Habsburgs go Protestant?
Is there any way of getting Friedrich and Albrecht to support a similar candidate? I would assume that the secularization possibility for Mainz would instantly draw Hohenzollern interest. The Pfalz Wittelsbachs were the electors for most of this period, so they would be the most important figure to consider of the two branches at least for the election.
There were branches early on who flirted with Protestantism, probably most notably Isabella of Austria and her husband Christian II of Denmark, though Christian later turned his back on it. Further, I read somewhere that Joanna "the Mad" had significant interest in protestant teachings, one of several reasonns she was kept from power. There are others, but I can't quite remember who. Most of them flirted with Protestantism, but I think it was exceedingly rare for any of them to actually convert.