supermarket club cards - Lemmings.world

Hey I’m sure you all know how sketchy club cards are for collecting your data. But I do begrudge paying slightly higher prices just for valuing my privacy. I was wondering if there was any way to sign up to these things whilst limiting the data they have access to. Would it be enough to sign up with fake details and never use their apps? Or should I just give up on this all together? Thanks!