It's a bit offensive to say people are "making use of getting offended", as if it was just an excuse to be awkward. Often times when someone says they have an issue with something, it's a genuine issue which might not seem that big to you because you're not living their experiences, but is still valid to them. In fact, using "coming out of the closet" for telling people you're a brony could have an indirect effect on LGBT people by devaluing the term and making it sound like it's not a big deal, when really it can be a huge deal.
More generally as regards the thread:
I don't find using coming out of the closet to be offensive per se, but I do find it to be a huge overstatement and that's where I have a bit of a problem with it. I realise that people do get mocked for being a brony and that the fear of how someone will react is genuine, but it's not the same as people fearing losing jobs, their home, or a relationship due to being LGBT. Also, being a brony is great but at the end of the day you don't have to wear brony shirts. You could leave the jewellery at home. You don't have to tell people in order to live your life comfortably. At the end of the day, you're telling someone you like a TV show that they might find hard to understand or make assumptions about, which can be hard, but it's not the same as saying "I want to be with other girls" or "I am male on the inside". For an LGB person, they have to risk coming out if they want to get married (if they're legally able to), live with someone, or even hold hands with their partner in public. For a T person, they have to risk coming out if they want to be able to present as their real gender without having to hide inside their biological gender for ever. So yes, I do think it would be better if bronies didn't use the term.