Are girls who are in relationships where the guy openly farts but the girl doesn't betraying women's rights?

You're taking things a little too seriously. If that man doesn't allow the woman to, that's a different story, but if the woman chooses not to, that's her decision. Making her fart in front of a guy is just as bad as not allowing her to. Each person should have the freedom to make their own decisions, no matter how small or insignificant they may seem.