I can understand that the older chess club kids might be tough on a kindergarten kid. But as our kids got older, if it was an activity they wanted to do, we told them it was not about being with your friends. You don't need to be friends with the other kids on the chess team, math team, baseball team, etc. You just need to be polite and respectful, and be a teammate.
My eldest played her sport with kids who were not her friends - she was not in that group. They seemed to be okay with her, but they were downright nasty to some other kids. When they were about to graduate HS, these kids apologized to her for being not so nice in their younger years (though my kid certainly didn't receive the worst of it from these kids). However, they were teammates on the field and worked together on the team (even placed 4th in the state in their sport one year). They just weren't buddies outside the team.
As for conflicts, there will always be conflicts with various activities. You can't always participate in all of the activities you would like to do. As kids get older, they often must choose one or two activities and drop others. Anyone who is seriously into math competitions, a travel sport or similar will quickly realize that these things take a lot of time. My kids play a travel sport and the tournaments consume every weekend in the spring/summer (and they have played travel since 2009). They also know kids who are very serious about math competitions, as in making USAMO (one kid did so every year from 8th grade on) - then it isn't just about padding the college application.
Now after I said all of that, I admit that middle kid did Mathcounts because of the friend thing. Her friend's dad was running the Mathcounts club/team and the friend didn't want to be the only white kid there. So she asked middle kid and one other friend to come to Mathcounts so she wouldn't feel alone. They ended up having fun - the dad does a lot of fun math projects and provides plenty of snacks. When middle kid was in 7th grade, a couple of the good team members were sick on the competition day, so middle kid and the other friend had to sub on the team. Turned out to be an all-girl team (two white kids and two Asian kids) and middle kid and friend hadn't really done much practice, but the team managed third place at the county level out of about 24 teams.
So if a kid thinks they might like an activity, tell them to give it a fair chance. They don't need to be friends with the other kids, just be a good teammate and treat others with respect. This might not be a good approach for really young kids, but once our kids hit 9 or 10, this was our approach (and I think it has worked out pretty well, at least for our kids).
