Turns out the problem was with me not being familiar enough with Buddypress. I hadn’t realized the “Accept” button only appears under /members/username/friends/requests/ and not in other places in the profile or member list.
I am running WordPress 3.01 with Buddypress 1.2.6 (just installed). My problem appears to be similar. Details follow.
The first time a user goes to the profile of the user requesting the friendship, the Accept and Reject buttons appear. However, if they do not click one of the buttons, then a greyed out “Friendship requested” button appears in all places where the “Accept” button would have appeared.
I have quite a few plugins installed, but none of the ones mentioned in this thread.
