Add Message button to user card and profile of logged out user

I’d like to add Message button to the user card and profile of logged out user. The UX choices are as follows:

I’d like to add Message button to the user card and profile of logged out user. The UX choices are as follows:

1/ hidden from the user
2/ visible but disabled
3/ visible but prompt for login/signup

We currently do 1. I’d prefer to do 3.

Users might need to contact a user for support, request access to a group, ask about a private matter, etc. A user might forget they are logged out so it’s just confusing to change the interface. For new visitors, it encourages them to set up an account. It hopefully avoids users adding an email address to their profile page.

I don’t think this hurts the goal to encourage public topics and replies. If the content is something that belongs in a private message, that’s not the kind of content you want posted publicly.

We currently do this with logged out users for the reply button and likes.