Am I Allowed To Exclude Certain 'customers' From My Business? [ca]

Cliff notes: We opened gym with adjoining juice/coffee bar, clientele from card/game/comics shop in same center come in and cause disturbances, behave poorly, have hygiene issues, spend no money, subsequently drive off our gym clientele. How do I legally address this without transforming my deli into 'members-only?'

My wife and I spent every penny we've ever earned, plus inheritances, plus loans, etc. on building out a health and wellness center, which includes a comprehensive gym space, yoga/dance studio, a classroom, a sauna, with an adjoining juice/tea/coffee bar. We just call it the Deli for short, as it was a shuttered deli before we took it over. This business is our life's work, and something we're extremely passionate about. We live in a very high CoL area where there is a greater focus on health and wellness and fitness, which is why we chose this particular location.

Here is the issue: In the commercial center where our business is located, there is a comics/games/card shop. We're having an issue where the game store's clientele are coming over to the deli in groups, taking over our patio and inside tables and playing card games, board games, etc. This isn't that big of a deal as we want to be welcoming and open to the community and hopefully use the deli as a way to promote our programs and memberships, however, these folks just don't spend any money, don't become members (even when offered trial memberships) and they frequently cause disturbances and it is severely affecting our paying membership clientele. We're over it. We just had someone have a full-blown crying episode and lock themselves in the restroom, and we don't know why.

We've been advised we can't prevent them from coming in, even though it's very easy to tell who is coming from the gym and who is coming from the game store. We've received a lot of comments and complaints over the last month over how the deli is filled with these young people and it is simply driving off our membership and desired clientele. Fortunately we haven't had any membership cancellations but we really want our juice/coffee bar to be a place our members can go before/after their workouts to replenish and refresh themselves, and they're being made to feel very uncomfortable. How do we handle this with grace? Can we really not just put up a sign that says "[game store] customers are not welcome at this establishment."?