I know there was something, but I didnt quite remember it clearly anymore, and hence simply wrote "by population" without going into details

And, IIRC, if the monarchy hadnt been abolished, Württemberg wouldve ended up with a Catholic ruling house, despite its protestant tradition and corelands. Heh.
But in any case it doesnt greatly matter. Religiousness was of course still important at the time, but cofnessional divide wasnt really anymore, or at least not in politics (everyday society is another matter). What mattered more were Badens quarrels with Bavaria and its economic competition with Württemberg.
Now as for Prussia going east: If its post-1815, i.e. with the western territories already gained, it would make zero difference. However, if it isnt "shifted west" in the Congress - well, it was still a Great Power. Lets not forget that. But it also was the weakest. Probably it would not have been able to challenge Austria at all. OTOH, its likely that Germany minus Austria would still economically band together, and then Prussia will still be the strongest among them. It would probably be a parallel co-existence of an increasingly unimportant German Confederation and an increasingly pulling together, EU-style, Zollverein equivalent.
And the Bavarian government WAS opposing Prussia. It was also the only southern state to actively do so and search for alternatives. Its just that there werent any. The idea of a Bavaria-led "Third Germany" was nothing short of absurdly unrealisable.