Thank you so much @vapvarun! This worked. However it still shows the WordPress logo when the sign-in/log-in page pops up; anyway I can avoid this, maybe by changing a theme or something along those lines?
I previously had Peepso, but I just deleted it completely and then I deleted BuddyPress as well and re-downloaded it, but still getting same issue. Any idea of which plugin it could be or should I try disabling everything? Or do you know of any other solutions?
I think the answer to my question is yes, you do need a WordPress account to log in to your BuddyPress account. However, creating the account using the “Register” button coming from the BuddyPress plugin seems to not actually be creating an account, since right after clicking on the confirmation email it redirects you the WordPress login and then when you type in the information you just used to create your account, it says that the user does not exist. Any ideas on how to fix this?