Labels are just words we use to collect and share bits of the world. A gay guy discovering he's not actually all that picky about gender should be able to start calling himself bi without fearing biphobic reactions (internal or external).

Biphobia, which is just a modern label for a collection of attitudes that predate our modern concepts of sexuality, would still be a thing if no one called themselves "gay" or "bi" (or pan), just as same-sex attracted people got lynched for going against some people's beliefs long before there were words for their attractions.

Labels aren't the problem. Dogmatic adherence to narrow concepts of gender and sexuality is the problem. It's helpful to identify the way I do so people who also identify that way can find me and compare experiences with me.

Labels for gender and sexuality are best treated as a way of finding others like yourself to increase self-knowledge and protect yourself against people who want to hurt you because of the feelings those labels represent.