A conservative shul has a swimming pool with co-ed swimming but has hours for men only. Can a man pay money to swim there during men’s hours? Is that considered supporting conservatism?
It seems to be permitted, and the fact that it is helping the temple is not an issue. Although we may not go into a conservative temple to pray, because it is a place of kefira, nevertheless it doesn’t have the same severity as a church, which is considered avoda zara, which we may not benefit it. However the swimming should not be during their prayer times, (if there are prayers during the week!) and evident that you are not going there to pray, but for other reasons.
See Igros Moshe Y:D 1-68 regarding making the blueprints of a church which are not allowed, but we are allowed to make the blueprints of a conservative temple. Also see Igros Moshe O:CH 3-30 regarding going to a wedding in the hall of a conservative temple.