Thank you for the help! I think I was being an idiot; it only appears to be occurring for users who have an account. Others are not seeing it. We can close out this topic, but thank you!
Thank you Simrandeep. I was able to find that setting in BuddyPress and disabled it, but it does not appear to have resolved the issue. I cleared my cache and checked the site, and the login menu is still there.
Thank you, will do. Feel free to delete the topic.