We can be aware of them without letting their existance hamper ours. It can be tough to bounce back. Periodically I run into self-congratulating bisexuals who insist that bisexuality is k00l because it means attraction to people instead of genitals. I wonder if these people know how insulting they sound. As much change as we've made in the recent past, it's still there.
Some people make the mistake of conflating bi and poly.
Sometimes I think I know. Sometimes I don't. But there are some bisexuals who, even though we feel that we can have relationships with either gender, and don't require both, still are aware of and revel in the genders of our partners. It's really not much different than picking up anybody else. To this day, this pair of bisexuals is still not quite sure.