I have no clue what "Barstool Sports" is or have any desire to find out after seeing this discussion. However, I can easily see a company having this policy signed by incoming employees if they know that their form of "entertainment" is going to be geared towards the raunchy side.
For instance, I would assume employees of Howard Stern sign something similar.
I actually don't have a problem with having people sign something like this. I would assume many people who are more liberal socially would agree that Howard Stern has the freedom of speech to do what he does.....as long as everyone involved knows it going in.
The company needs to make new employees very aware of what the job entails before they are exposed to it. Then, if the employee agrees and starts the job, they were warned.
I don't see specifically having someone sign this as evidence of sexism. Now, you can say the show or entertainment itself is evidence....but the document....no.