Habeck is a realo, not fundie. Support for him among green voters (which is what actually counts, not party members, he’ll get his nomination because who else should they run) is overwhelming, very good among SPD voters, AfD voters hate him and that won’t change any time soon, CDU is where he’s going to have to make inroads. Perception-wise the problem is competence, blame that on the Bild campaign and I absolutely expect that to shift very quickly once people actually hear him in a debate.
Just for the record, and context: That wasn’t misogyny, it’s not calling any woman anything (though using a word vulgarly referring to female genitalia), it’s the established insult for Merz. Really doesn’t translate well, not so much word-wise but connotation and implication-wise. Cf. the American vs. English vs. Australian usage of the word, doesn’t translate at all and that’s within the same language.
It’s an imputed high-school nickname calling him, in my reading, an immature braggart. You know, 12yold brags about their extensive sexual experience, gets called “pussy hunter” in return to make fun of him. There’s also the additional linguistic quibble that the word, to the amusement of the rest of the republic, simply means “face” in Bavarian and can be used there more or less in the sense of “gob”, as in “shut your gob”. He indeed has a big one.