This isn't even a real matter of debate. The only way one can respond "No" to this question if one is informed is if one either thinks that institutional dominance of heterosexual and cis-gendered people is not just acceptable but actually preferable, or if one just doesn't think discrimination matters very much.
Gay people only got equal access to marriage in 2015. "Don't Ask, Don't Tell" was only repealed in 2011. Is it really that big of a surprise that we have a society that still has a deep vein of homophobia and transphobia within it?
In 2016, we've seen bathroom bills to force transgender people into bathrooms where they will frequently not look like they belong and make people afraid for no good reason. It's part of what I call "sadistic busybodyism": so many Americans want so badly to hurt and constrain transgender people that they just don't care that they are actually creating the nightmare scenario they envision. They don't care that there are more confirmed cases of Republican representatives engaging in bathroom sexual misconduct than transgender people, or that transgender men look like attractive women who just walked into a bathroom which may cause them to be a target of potential sexual harassment and assault, or that transgender people are immensely more likely to be the victims of sexual assault than the perpetrators, or that the bill can't be enforced and that the process of enforcing it would mean more male cops in female bathrooms, or that the hysteria that was being produced to try to win elections was leading to real people being harassed out of bathrooms even when they weren't trans. They don't even care that big burly guys will walk into women's bathrooms, forced to do so by the law, and make the women inside afraid of being attacked.
Sure, many of these people claim that they're just afraid for their children being attacked in the bathroom. But there comes a level of hysteria, fear and ignorance that ceases to be about any kind of love and is about hate. Rape is still illegal. Why would a person who intended to assault someone and commit a felony be stopped by an additional misdemeanor or even felony charge?
The evidence for institutional homophobia is just staggering. The level of discrimination is high enough that gay men make less on the dollar on average. As many as 43 percent of gay workers and 90 percent of trans workers report discrimination on the job. Transgender people still face serious discrimination in the military. (And while I have major problems with the colonialism of the American military, we as a society should insist that those who want to serve are able to do so unless there's a compelling reason that they can't. And yes, the ban on their service has just been lifted). Gay and trans students still face constant homophobia.
And that's the U.S. Need I mention that things aren't so great in Russia? Saudi Arabia? Uganda?