Gay rights advocates have been upset by the brief, although you'd be very hard pressed to find out the main reason why from the news reporting and DOJ PR about the issue. The problem is not so much the fact that a brief was filed in support of DOMA but the language and arguments used in the brief. As David Link put it:
It is gratuitously insulting to lesbians and gay men, referring (unnecessarily) to same-sex marriage as a “form” of marriage, approving of congressional comparisons between same-sex marriages and loving relationships between siblings, or grandparents and grandchildren, and arguing (with a straight face, I can only assume) that discrimination against same-sex couples is rational because it saves the federal government money. There are some respectable arguments in this motion, and this kind of disrespect is offensive.
Yet the DOJ statement in response to the public outrage pretends otherwise, defending their actions as if it was the decision to file a brief alone that was making gay people upset:
As it generally does with existing statutes, the Justice Department is defending the law on the books in court. The president has said he wants to see a legislative repeal of the Defense of Marriage Act because it prevents LGBT couples from being granted equal rights and benefits. However, until Congress passes legislation repealing the law, the administration will continue to defend the statute when it is challenged in the justice system.
Nor is the anger over how the DOJ supported DOMA in their brief appearing in mainstream media reports: CBS simply states "Gay rights groups are upset that Obama appears to be going back on his word [to repeal DOMA]. But the Justice Department says it's following the standard practice of defending existing law", with no indication of the main problem identified by prominent gay rights advocates such as Andrew Sullivan that "the question is not why the DOJ should defend existing law; it is why they chose to lard it up with such egregious anti-gay rhetoric and religious right arguments"
It is very hard to put forward your case about why something is hurtful to you when the very reason that it is so hurtful is not being made known. No wonder you get people claiming that gay people get "hysterical" over things. If I was seeing someone getting really mad and upset just because a brief was filed in a court case, I'd probably think they were hysterical too. But that's not the root cause of the anger here: it's the actual callous language in the brief that's at the heart of the matter. And yet, I fear, most people will be completely unaware of that, thanks in no small part to the PR actions of the DOJ itself.