Forgiving him depends on a lot of factors. If he is truly remorseful and willing to work on the relationship, it might be possible. But it won't be easy and will take time.
If you've caught your husband in such a situation, first, take some time to calm down. It's a very shocking discovery. You could consider having an open and honest conversation with him about why he did it, your feelings, and what it means for your relationship.
There is no evidence to suggest that such activities occur in a gym environment. Gyms have rules and ethics in place to maintain a proper and respectful atmosphere for all members. This kind of description violates the basic norms of a public fitness place.