I'm no 'homophobe' either but I could kind of put myself in the OP's shoes. Gay days is a celebration of sexual orientation which might lead one to naturally wonder whether they'd more likely see shirt slogans, actions or other things related to sexuality that they'd rather avoid with their kids. Of course there are gay people at WDW every other day and they're not acting any differently than straight people BUT those days aren't designated as a big gathering to celebrate a certain kind of sexuality. Heterosexuality, homosexuality and bisexuality aren't about what you look like, your favorite hobbies, or a love for certain kinds of food. It's about your preference for who you are intimate with.
Also, for those who haven't been to WDW during Gay Days, how else would you know whether it's tame or like a pride parade at many other gay festivals? (Around here anyway, pride parades can get pretty wild and you see some things that aren't exactly G rated or part of everyday life.) You know by asking, which the OP did.