On your Facebook user interface, there are recommended pages for you to like. Facebook displays these based on what they believe your interests are as well as the interests of your friends. Facebook often displays a message that says “Friend likes XYZ Product” and it gives you a link to click to like that as well.
Advertisers pay Facebook to get others to click and like their product or service, and you could unknowingly (now you know) be used to “endorse” a product or service to your friends if you like something and that company spends money on advertising. This is generally no big deal, as I don’t really care that people know I am a New England Patriots fan or that I like Torah.com.
There are many gTLD extensions that are special interests, such as .Democrat and .Republican. Many of us know people and companies who are vying for these extensions, and we might think it’s a friendly gesture to “like” our friends’ TLDs. I might think Frank Schilling’s a good dude so I’ll “like” his Facebook pages without really thinking about what they are.
If I saw that a domain industry friend “likes” the .Democrat and/or .Republican TLD page, I wouldn’t think twice about it. I’d probably assume they are doing a friend a solid by supporting a page (plenty of my friends “like” the Lowell.com Facebook page despite not ever visiting Lowell). However, people outside of the industry may not think about the TLD but would think about the special interest.
While most gTLDs are fairly innocuous, there are some that are hot button issues. For example, it might lead to some embarrassment if someone “liked” the .HIV page and they were being used by Facebook to “endorse” the page to their friends. Even pages like .Democrat might cause issues for someone with strong political views.
I have no idea when gTLD registries will begin creating Facebook pages to promote their TLD. I also don’t know if they will be advertising. You should know that when you “like” a page and the admin of that page advertises, you might be used in advertisements, and that could be embarrassing.