I'll take each comment piece by piece.
Someone flaunting fairy wings
"Fairy" is, historically, a derogatory term for gay men. Fairy wings a.) reclaim the term, and b.) serve as a counterprotest to the challenging of LGBT identity. By saying people shouldn't wear fairy wings is to, metaphorically, put someone back into the closet.
Makeup, drag, etc. also serve as a counterprotest to the challenging of LGBT identity. By saying people shouldn't wear heavy makeup, you're (ignoring the inherent idiom) literally saying to go back into the closet.
They are ripe to ridicule.
The fact that you think it's okay to ridicule appropriate presentations of LGBT identity that serve as a political counterprotest to LGBT erasure/denial is homophobic, whether you intended to do it or not.
It's also okay for people to just have fun.
My point is, why are they making a cosplay if they are not like that every day?
Exaggeration is an effective counterprotest. That's also like saying, "Why do a parade if you're not going to do a parade everyday?"
There's carnival for that.
A carnival doesn't deal with the issues of LGBT rights and identity, so you're missing the point of Pride.
And also, now that we are on the subject, should someone care if other people are gay?
No one should be bothered by it, if that's what you mean by "care," but it's also part of one's identity.
That's like saying that no one should care if I'm male. It's true that no one should be bothered by it, and it's true that no one should dwell on my sex and gender too long, but being male is also an important part of my identity, and a person who doesn't know that I'm male can't know me as well as someone who does know that I'm male.
Given the aforementioned issues with the denial of LGBT identity and LGBT-erasure, it's also extremely important for people to know about one's LGBT identity. For example, if you don't know anyone who is openly gay because nobody talks about it, then the plight of the gay community is just as invisible.
Why do gay people need to come out of the closet?
In addition to the aforementioned LGBT identity issues above, gay people often need to come out of the closet because they are outwardly indistinguishable from straight people. Black identity is important to people of color, but they usually don't need to come out because it's outwardly apparent.
Who put them there? I find this kind of thing confusing, because straight people don't make a press note about it.
Society put LGBT people into the closet because the assumption (rightfully or not) is that someone is straight, since so many people are straight. If we didn't assume a person's sexual orientation, identity, etc., then everyone would have to come out.
Straight people don't have to come out because they fit the default assumption, so there's no misinformation to correct.
Your freedom as a gay person fades as soon as you give explanations to others
I'm not sure what you're talking about here, but if a person loses any freedoms from coming out to others, then there's a problem, and that problem is more than enough reason for the need for Pride.
Just be. Live and go out with your partner.
The aforementioned discrimination against LGBT people, violence against LGBT people, prejudice against LGBT people, and LGBT-erasure are obstacles that get in the way of this goal, hence the need for Pride. Certain people don't want to let LGBT people "just be." That's the point.
Or do you need to tell the world that you love someone because your genitalia match?
Saying a person shouldn't acknowledge to the world that he or she loves someone with similar genitalia is LGBT-erasure, and you can read above for the issues that brings.
Let the world adapt to you instead of the other way around.
The world cannot adapt to LGBT people if they're invisible, hence the need for coming out, Pride, etc.
That kind of social inertia needs to disappear ASAP.
Then you should be an LGBT ally and support Pride.
I know, for instance that I shock people by being so uncaring about one's sexuality (seriously, people already told me that).
It's one thing to not be bothered by it, if that's what you mean by "care." It's another thing to be blasé about it as if it's unimportant to the person's identity. You can see above for why straight people don't have to come out.
I just don't care who you love
That sounds inconsiderate and as if you don't care about someone. Imagine saying that to your friend after he tells you he's seriously dating a new woman or getting married.
I guess a person's identity really isn't important to you, because that's not my name.
I just find some people there have a bad taste in clothing...
Throwing shade about people's stylistic choices? Perhaps you belong in the Pride Parade.