Mages guild is dead
replaced by secular and another group Synod and whispers no? who knows what they are doing this time around
That just means we get to have two guilds for mages in Skyrim, maybe, it may also be that some time between Infernal City and Skyrim, one of these groups was disbanded or they combined again or something, who knows what can happen in over a hundred years, or maybe both factions exist at the time of Skyrim, but only one is actually joinable in the game, either because the other one has no presence in Skyrim or exists as a faction in the game, but isn't joinable, we really can't say what Bethesda will do.
Like in Morrowind, it made no sense to join both the Mages' Guild and the Telvanni, and they had different views. The guild saw magic as an area to study and improve themselves through research. The Telvanni saw magic as power, the more versed you were in the magicka schools, the more powerful you were.
And yet you could join both, I'm not sure if this would ever cause problems for you or not, but one faction would not prevent you from joining entirely if you were part of the other, the only factions that did that were the Great Houses, I'm pretty sure.
But really, the entire problem being discussed here could be adressed if skill requirements for factions were returned, or alternately, it would be much better if the Mages Guild quests just actually required you to use magic, that way, it would make much more sense than how it was in Oblivion, since by succeeding in those quests, you'd have proven that you can use magic, it would be sort of like the Thieves Guild in Oblivion, technically, you're not required to be good at stealth to join, but most of the quests require you to rely on stealth, so the actual numbers aren't what controls whether you can advance, but whether you can show that you actually can do what the guild needs you to do or not, and honestly, that actually seems to make more sense. Your guild can't see what your skills, after all, what they'll be looking at is results. The problem is when you don't need to know anything about the skills the guild specializes in to get those results, like Oblivion's Mages Guild. At least for the Fighters Guild, while you didn't actually have to be good with a sword, you had to be able to fight with SOMETHING, even if it was magic.
But it's been indicated that Bethesda is planning some major change with the factions, so we really can't say how they'll be handled, we can only wait, and see what they do.