This question reminds me of two articles I've read in the past.
There is a PsychologyToday article that does suggest and provide research to back the idea that conservatives tend to be healthier and exercise more. One of the studies cited in the article is correlational and does not provide a causal relationship and, as the article points out, leaves the definition of terms like 'conservative' and 'liberal' up to interpretation, but it found that conservatives tend to have better self-reported health. Another study found that conservatives were more likely than liberals to use the stairs than the elevator. The article discusses further studies that suggest that people primed to be conservatives are more likely to value personal responsibility and people who self-identify as conservatives are more likely to score highly on conscientiousness.
https://www.psychologytoday.com/us/blog/unique-everybody-else/201902/are-conservatives-healthier-liberalsSo in other words, if you take this at information at face value, it does lend credence to the idea that individuals with conservative views would be the ones more likely to go to the gym and work out. At the same time, the author also explains why one of these studies is flawed (I won't go into detail about it here because it would be too much typing, but you can read for yourselves).
Another article discusses a study with a slightly different conclusion though. In this one, the more extreme your political orientation is (either toward the left or the right), the higher your level of fitness is likely to be. Centrists are the least likely to take care of their health, according to this study. The article attributes to this correlation as being due to apathy in life amongst centrists extending to apathy in fitness.
https://www.esquire.com/news-politics/news/a32284/political-preferene-determines-fitness-level/So, somewhat interestingly, it may be true that people who take fitness & the gym seriously tend to be Republican voters, or maybe it could be anyone at more hardline ends of the political spectrum, or both (maybe people on hardline ends of the political spectrum take fitness more seriously but conservatives in particular). It's an interesting subject to look into.
