It seems like quite a few people have been having problems liking or commenting on other WordPress bloggers’ posts. It may be an issue with your browser settings that stops the site from recognizing that you are in fact signed in to WordPress.
If you’re using Safari, go to “Preferences” in the “Safari” menu, then the “Privacy” tab. “Prevent cross-site tracking” needs to be unchecked.
In Chrome, go to “Preferences” under the “Chrome” menu, then scroll down to the “Privacy and security settings” and click on “Site Settings” then “Cookies and site data”. “Block third-party cookies” has to be turned off.
I’m not sure about Internet Explorer and other browsers, but it would probably still be an issue related to needing to enable cross-site tracking and/or third-party cookies. These support pages on Microsoft’s site may help:
Hope this helps if you’ve been having issues!