Yes it's possible, despite the answers above. If you want to keep the websites completely separated, you can with WP Remote Users Sync (disclaimer: I am the author of the plugin)
Edit - to elaborate on the context and method used as asked in comments:
The way it works is that each time there is a change in user data (login, logout, create, update, delete, roles, password, metadata, using WordPress hooks and by redefining pluggable functions), a call is made to all registered remote sites (using a
<script> tag for login and logout, so that cookies can be shared, and
wp_remote_post in all other cases) using a specific endpoint (
my-website.com/wprus/[action_name]). Then, on the remote site, the calls are listened and caught, the data is parsed, and the users are synced.
What sets this plugin apart from what already exists is the security layers in place: Communications are encrypted with single use initialization vectors, hmac-signed, token-validated and IP-validated to make the process as secure as possible.
What pushed me to implement it is that either the solution did not exist, or even commercial solutions out there were not suitable (the most popular and biggest offender being Share Logins Across Multiple Sites which is up to 250 USD per year and yet vulnerable in many ways, worst of which being iframe injection, but more info on that is worth its own dedicated post).
Syncing websites using separate domains, databases, and servers (and more so with secure token exchange) also means that there is an unavoidable marginal performance overhead for each user-related operation for each connected remote site (remote calls).