In BG 1 Dorn I-Khan and Baeloth also decreased reputation score. I think it has to do with how well-known those characters are in the realm.
I think players could go the Astarion route and embrace the infection. That way they look to Minthara for guidance with the Absolute, particularly if they want to role play a curious neutral evil or spiritually dejected character.
I had the thought of taking her prisoner before too. Her connection to the Absolute is interesting and would be a good source of intel.
I'm not that familiar with the EE companions, apart from the monk, I didn't really use them. But it makes sense, since Baeloth is a drow too and I think Dorn is some kind of anti paladin?
About the Astarion route: I'm all for it. I think, there should be additional dialigue with Gut (since she is the spiritual leader) about it. I could go behind that, good idea.
Taking Minthara prisoner could give you a bit more insight. Maybe she won't become a companion, but an unwilling camp follower that way.