An interesting stab at a number.
The author of the New York Times piece comes up with roughly 5% (Note that he assumes that there are gays and then there are straights and nothing in between):
There are three sources that can give us estimates of the openly gay population broken down by state: the census, which asks about same-sex households; Gallup, which has fairly large-sample surveys for every state; and Facebook, which asks members what gender they are interested in. While these data sources all measure different degrees of openness, one result is strikingly similar: All three suggest that the openly gay population is dramatically higher in more tolerant states, defined using an estimate by Nate Silver of support for same-sex marriage. On Facebook, for example, about 1 percent of men in Mississippi who list a gender preference say that they are interested in men; in California, more than 3 percent do.
Are there really so many fewer gay men living in less tolerant states? There is no evidence that gay men would be less likely to be born in these states. Have many of them moved to more tolerant areas? Some have, but Facebook data show that mobility can explain only a small fraction of the difference in the totally out population. I searched gay and straight men by state of birth and state of current residence. (This information is available only for a subset of Facebook users.) Some gay men do move out of less tolerant states, but this effect is small. I estimate that the openly gay population would be about 0.1 percentage points higher in the least tolerant states if everyone stayed in place.
The percent of male high school students who identify themselves as gay on Facebook is also much lower in less tolerant areas. Because high school students are less mobile than adults, this suggests that a gay exodus from these areas is not a large factor.
We can approach the question of whether intolerant areas actually have fewer gay men another way, too, by estimating the percent of searches for pornography that are looking for depictions of gay men. These would include searches for such terms as “gay porn” or “Rocket Tube,” a popular gay pornographic site. I used anonymous, aggregate data from Google. The advantage of this data source, of course, is that most men are making these searches in private. (Women search, too, but in much smaller numbers.)
While tolerant states have a slightly higher percentage of these searches, roughly 5 percent of pornographic searches are looking for depictions of gay men in all states. This again suggests that there are just about as many gay men in less tolerant states as there are anywhere else.
Read more here.
And this graphic is very telling.