Arguably, I flaunt my hetero-sexuality more by kissing my lover in public than many homosexuals are comfortable doing for reasons of personal safety.
One cannot argue that exhibitionism (parades, magazine covers, etc) is a homosexual trait. You may not "flaunt" your sexuality, but I'm sure you do flaunt something else at some time or another, whether it be your vocabulary, your politics, your feelings on animal rights. When it comes right down to it, everytime you open your mouth, you are going to offend SOMEONE somewhere.
Is it fair to say that a woman should not express any sexuality in public just because she likes women (I'm not saying anyone said this, but it is the logical end)? Are you willing to go to the same extreme to not offend her?? Perhaps she does not care to know you are heterosexual, perhaps this idea offends her?