I am so glad you asked this question! I've been waiting all week for this.

So, the short answer is that the film is accurate. There are a lot of finer points to discuss, however. First off, I want to contextualize the film and its source material. The Normal Heart was a play by Larry Kramer that was first performed in 1985. It is a lightly fictionalized retelling of Kramer's experiences in the early years of AIDS, and the organization he helped found, Gay Men's Health Crisis (GMHC.) It is very much one man's personal experiences, and must be understood as such. It was also intended to be a piece of agitprop that would help mobilize the gay community around AIDS. This adaptation had a screenplay also written by Kramer; it is largely faithful to the play, but adds in some new material and makes a few other small (but sometimes significant) changes. So keep in mind that this is not a 'film about the AIDS crisis' but an adaptation of a play that was written in a particular time and place.

So in terms of government (lack of) response, TNH is spot on, which I think is part of the reason it has taken so long for this film to happen. It paints a pretty unflattering portrait of the straight world; a portrait that is, by and large, completely accurate. Government organizations, and the heterosexual and closeted homosexual people who ran them were deeply reluctant to get involved in what was seen as a "gay disease." It's easy to forget, knowing what we know now, that when AIDS came on the scene, it completely baffled everyone. From a purely medical perspective, HIV is a tricky little bastard of a virus, and AIDS is a weird and puzzling disease. Although AIDS came to affect a large swath of the gay community (as well as the heterosexual world) quite a bit of the initial reporting on the disease focused on gay men who a part of the gay 'fast lane' - men who had hundreds of (unprotected) sexual encounters a year, who frequented bathhouses, and who engaged in kinky sex like fisting or S&M. From the beginning AIDS was tied to "non-standard" sexuality and "deviant" sexual practices. The eighties were a conservative time, and social and religious conservatism were profoundly influential in shaping the national discourse. For some on the religious right, AIDS was seen as a kind of divine retribution for acts against god. Even for folks who may not have gone so far in their personal beliefs, showing support (and thus tacit approval) for people with AIDS in the form of political action had the potential to be very damaging to a person's career. For closeted men and women in power, the 'risks' were even greater. Many were so fearful that anything less than strong anti-gay and anti-AIDS funding view would 'out' them and cause the downfall of their political careers. TNH refers to the then-mayor of New York City, Ed Koch (his name is never explicitly mentioned in the play) who was a closeted gay man who went a long way in avoiding AIDS out of fear of being perceived as 'too nice' to the gay community, which might draw attention to his status as a 'confirmed bachelor.'

In regards to behavior/views of the gay male characters, it's also quite representative of the time. Again, this a retelling of Kramer's experiences. Several of the characters are direct analogues of real people; I imagine even those who are no are based on real people to some extent or another. This is another situation where it's easy to forget the subtle but massively important changes in the gay experience in the last thirty years. The gay lifestyle of the post-Stonewall pre-AIDS days, with all of the corresponding 'excesses', was very much centered around sex and sexuality. The character of Mickey in TNH (played by Joe Mantello in the film, who played Ned Weeks in the 2011 Broadway revival that paved the way for this film) does a great job of situating and explaining the attitudes of a lot of gay men at the time. So much of the idea of gay liberation was centered around the right to express gay sexuality in a way that was uninhibited and free. Men of this generation almost universally grew up in the closet, often thinking they were the only one of their kind on earth. When they learned that there was a word - homosexual - for what they were, it was invariably used in a negative context. When these men came to a large urban center in the 70's they discovered a world where they could be themselves. A place where their true selves were celebrated - not merely despite their 'deviance' but because of it. For gay men in the 1970's, sex was not just sex - it was a political act that signified the gay man's liberation from the oppression of heterosexual society. Mickey gives a great speech that expresses that view. It's great in the film, but a few lines were left out that I think provide a good context: "We were a bunch of funny-looking fellows who grew up in sheer misery and one day we fell into the orgy rooms and we thought we'd found heaven. And we would teach the world how wonderful heaven could be. We would lead the way. We would be good for something new."

There are a thousand and one other things I say about The Normal Heart, but I'm going to leave it at this for now. I'm very happy to answer any other questions or provide any other context on the play/film.
EDIT: I fixed the formatting. Spaces are good. Also grammar.