And the answer is, it depends.
And I hate giving this answer because it really doesn't answer anything, so let me elaborate a little bit.
The important thing is why are you thinking about protecting your hashtags?
And if your answer is that you will be able to stop other people from using it on Twitter or on Facebook, then it won't work because the use of the hashtag is not regulated by trademark laws. It's like I can use any brand name as an example or in a book describing anything about that brand. So, when I say I love to eat at McDonald's, McDonald's can't sue me for using their trademark. Even if I say I don't like to eat at McDonald's, they still won't be able to sue me for using their trademark. It's not a trademark infringement.
So even if you trademark a hashtag, you wouldn't be able to stop people from saying good or bad things about your brand.
But in certain cases, it does make sense to trademark your hashtag if the hashtag is how people know about you, what they think about when they are thinking of you. So if you've developed a hashtag that everybody associates you with, then that would be a good idea to trademark. But again, don't trademark it simply because you think that you'll be able to write a letter to Twitter and say, Oh you know what, these people are saying bad things about my brand and that's my trademark. That's not gonna work.
Disclaimer: Please note that this post and this video are not and are not intended as legal advice. Your situation may be different from the facts assumed in this post or video. Your reading this post or watching this video does not create a lawyer-client relationship between you and Trademark Factory International Inc., and you should not rely on this post or this video as the only source of information to make important decisions about your intellectual property.