So imagine a woman on stage, picture of some dude with a blot over his face and 'BASTARD' written on it.
- Sexist? Not sure it would indicate the speaker hates all men per se, just this one.
- But lame, like the speaker couldn't control themselves over their anger at someone and had to bring it on stage for some kind of pathetic vindication? Sure.
I'd advise not doing this not because it's sexist, but because it makes the speaker look like an angry, sad individual.
PS. If the hot sauce was glass, that's obviously even worse. Lesson: stupid drama (like throwing some ex girlfriend on an unrelated talk) invites more stupid drama (like throwing bottles at someone rather than using words as a first resort).