I don't think you're being irrational. I'm a single founder and it sounds to me like these guys are hunting for "tech help" on the cheap while trying to clear out potential competition -- otherwise, why the admonition to ditch your product?

Listen to your gut instincts. You might learn something about your market by meeting the competing team although it will probably be a waste of time. But it seems foolish to abandon your own plans in order to join some random and profitless company that has decided joining a no-investment incubator is a good deal. If money is an issue wouldn't you be better served just getting a job at market rates and continuing to work on your business part-time?

If you think there is some value in the community, you can always offer to advise some of their teams as a mentor in exchange for access to group events.