It is possible if you have the profile link or know the user’s Metamask address. This address can be manually pasted into the address bar in the browser after the /profile/ in URL. Note that this does not depend on whether you are logged in or not as the profiles are public.
Similarly, if the user whose profile you want to see has a nickname (the default nickname “Anonymous” will not work) you can paste it into the browser’s address bar after /profile/ in URL.
Other than that, there is no way to browse through the profiles at this point.