That all depends on how you're trying to get access. For example, if you are flying on AA but have a UA RCC membership, there is no problem using a RCC somewhere even when you aren't flying AA. But trying to get into a US lounge won't work because your RCC membership only allows access when you have a same day US boarding pass. DL/CO/NW all allow access to each others lounges for lounge members regardless of same day travel, but trying to use that NW WC membership to get access to an AS lounge when you're flying some other carrier won't work.