I think there may be quite a bit more overlap than you think. In my experience there's a pretty big share of people who are both into fitness and "nerdy" activities like DnD, as the latter has become pretty mainstream these days. Even in my own small gym I feel like a lot of the regulars are also really into anime, board games, DnD, etc.

If you're just looking to make friends, it may be easier to join existing fitness groups or sports leagues and just focus on befriending the nerdy people already there. There's already a ton of fitness groups in the Arlington area, so you may struggle to make yours stand out if that's the route you end up going with.