Girlfriend is angry at me for spending time with my ex, but that's not the way it is...?

Basically my ex girlfriend and I share a great deal of interest in the outdoors. We're both members of the same club that plans weekly trips to do things like kayaking, bicycling, mountain hiking, etc. So even though we're split I still see her often. This makes my girlfriend furious. She accuses me of doing more with my ex than I do with her. I've begged my girlfriend to join the club and do these things with me, but she's just not into it. Meanwhile it's not like I'm with my ex alone. There are fourteen people in the club, and we're all there having fun together. I've explained this to my girlfriend. I can't tell my ex to quit, and if I quit there's no other club like this around. But my girlfriend just doesn't get it. Somehow she sees this as practically cheating, which I think is stupid. Am I wrong?