Since they are not in the porn industry there is probably no valid case.
Example of a similar situation:
http://www.mcdonaldsfurniture.com/
If McDonalds (the fast food chain) could take out sites like this, they would. The fact that they are in a different business will protect them.
Nissan computer (nissan.com) is another popular example, although they definitely put him through the ringer trying to take it from him, but ended up having to pay his costs.
Now they are trying to obtain a trademark relating to computers so they can take it from him.
I never checked the site out fully, but if they are offering porn on it anywhere, then you should be able to take it from them easily.