Originally Posted by tjcxx

It is allowed to do what you are asking. I have done it myself, but not recently. Perhaps to the point, not since I had a physical AA Advantage card. I have not tried it since having to show membership and status on an app.

EDIT - to add that at lounge entry they may well want to switch your FF programme to AA. But you don't have to let them.
Also, I've successfully used the AA card for boarding groups. Again not recently: before boarding groups were printed on the boarding pass.