As the others already said, it's more a rural vs urban thing but yeah the south and especially bavaria is more conservative than the north or south (but the most conservative like you discribed with the stickers and all are living in east Germany except Berlin, cause Berlin is mostly a left oriented stand alone city). If you're non white there would be at least a lot of staring, sometimes worse (spitting, shouting,...) mostly everywhere in Germany.

If you consider munich it shouldn't be a problem as long as you don't live in a village around the city. Cause Munich itself has a left political party for I don't know how many years. That's why mostly every other south Bavarian outside of Munich has the opinion that Munich doesn't count as Bavaria. And as mentioned by others before Munich has some good queer stuff and the pride parade is one of the biggest in Germany and EU. I think this year around 500k people came and celebrated (Munich itself has ~1.4 million residents), but Munich doesn't compare with Berlin(east), cologne(west) or Hamburg (north), but it's still pretty good and the nature around munich is great!

So I would say if you really wanna live in a city it's nothing like the crazy people you seem to have right now, but it's not all happy sunshine as well and especially munich is expensive and one big bummer are the German people as well (cause we're so stiff and not really open to someone new).