As far as real life goes, traditional gender roles are what works best. There is no rational argument against that. Japan understands that. America used to.

But as far as fiction? Worldbuilding is far more important. We know so far that male Viera cannot be distinguished from female Viera until puberty, and the males only visit the females to trade, pick up the adolescent males, and mate. We also know that Viera in general do not leave the Wood unless they're okay with never, ever being allowed to return (this is a callback to FINAL FANTASY XII). It could be that male Viera eschew adventuring because their culture places so much emphasis on staying in the Wood. It could be that they're as rare as male Mithra in FINAL FANTASY XI, and therefore feel that "stay in the Wood" aspect of their culture even more keenly than the women. We don't have much more on lore here.

To say that the genderlock on the Hrothgar and Viera is "homophobic," "disrespectful of the LGBT community," or anything else to that effect is absolute freaking nonsense and must not ever be taken seriously, especially because people these days are offended just as easily by leaves falling off the trees in autumn.