Try to make sense of this if you can. The other day, a fund-raising event for the Democratic presidential candidate Pete Buttigieg, who is gay, was disrupted by protesters. But they weren’t the kind of protesters you’d expect to get angry about a gay candidate. The protesters were gay themselves. It was a protest against a gay man staged by gays. It was gays against gays. It was pink on pink. It was confusing.

The point the protesters seemed to be making was that Mr Buttigieg isn’t the right kind of gay. One of the activists said Mr Buttigieg needed to be more radical. “I’m proud of the fact a gay candidate has made it this far,” she said, “but it’s hard to enjoy or appreciate when his stances are so middle of the road and speak to a predominantly white, upper class audience.” What I think she meant is she doesn’t want a gay candidate, she wants a queer candidate.

I realise this might seem confusing to anyone who doesn’t follow gay politics closely, but this actually affects us all. There are cultural battles being fought over identity, sexuality, race, and gender, and they are starting to affect ideas that we used to take for granted, such as the idea that a gay person progressing in politics would be a positive development. Mr Buttigieg has a decent chance. He might be America’s first openly gay president. This would be, I hope you would agree, A Good Thing.

The fact some gay people do not agree is fine on the face of it. In fact, seen from one angle, the protests against Mr Buttigieg in San Francisco last week would seem to reflect the fact gay people have a range of views from conservative, to liberal, to radical, just like everyone else does. Gays waving placards at gays is a good thing because the issues matter more than the sexuality of the people debating them.

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However, on another level, I think the protests actually expose something else entirely; something more troubling. Superficially, the Buttigieg demonstrations look like they’re just a bunch of people falling out over issues like healthcare and education. But, instead, I fear it’s people falling out over labels and being intolerant about what, and who, can be included in, or excluded from, those labels. Which is pretty much the 21st century disease isn’t it? Progressives being prescriptive.

The specific label in question in the Buttigieg case is “queer”. There was a time not so long ago when the word queer was a slur shouted out in playgrounds or whispered behind backs, but for some gay people (but only some) it has now become more positive and preferable to the word gay, and is associated with a leftist, radical, anti-establishment ideology.

The concept of queer, according to its subscribers, is also in direct opposition to what’s called hetero-normativity and everything that apparently goes with it: man-marries-woman, man gives woman away, man and woman do what is expected of them by society. This is why the protesters were angry at Mr Buttigieg (Harvard graduate, naval officer, management consultant, moderate) because, although he’s gay, he could pass for a hetero-normative man and seems to behave like one in many ways (apart from marrying another man of course). The protesters weren’t complaining about the fact he was gay, they were complaining about the fact he wasn’t queer.

In some ways, I understand where the protesters are coming from. In the last few years, gay bars have been closing down, gay people have been getting married and having wedding lists at John Lewis, and the fear among some is that acceptance, welcome though it is, will homogenise the community and the dominant colour in the rainbow flag will end up being grey. Gay people, in other words, will become grey people and all start to look a little bit like Pete Buttigieg.

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However, the problem with this kind of approach is that the whole premise of queer relies on some profoundly misleading assumptions about gay people, specifically that because you are gay, you are, or should be, radical, progressive and left wing. Like it or not, gay people are just as likely to be conservative as straight people – in fact, Ivan Massow (businessman, former candidate for London mayor, gay, and Tory) was right when he said that, of all the political parties, the Tories are the gayest. And anyway, in American terms, Mr Buttigieg is unquestionably a liberal.

Railing against people like Mr Buttigieg for being middle of the road or non-queer is also counter-productive and confuses the argument over gay rights. Many of the gay Democrats who don’t support Mr Buttigieg are uncomfortable about his association with traditional institutions, such as the military or the Christian church, or the 40-plus billionaires from whom he has received political donations. But the involvement of gay people in those institutions is central to the struggle for equality – what, after all, could be more traditional than marriage? Equality must mean the right to be married if you want to be, and to be in the military, or indeed to be a little bit middle of the road.

In being so middle of the road, Mr Buttigieg may in the end prove another important point, which is that a lot of the labels we casually use, particularly on social media, are pretty crude and useless. Some people have labelled Mr Buttigieg rich, or upper class, or elitist, or a white man, as if any of these labels explain anything. In fact, Mr Buttigieg will have spent a lot of his life trying to come to terms with his sexuality and the difference it created with the people around him. He will have struggled to find acceptance in his own way and it doesn’t help when other gay people appear to judge his level of gayness, or suggest he is not gay enough.

I understand that for some gay people, the acceptance, or in Mr Buttigieg’s case, the apparent assimilation, can look like a compromise too far, or a diminution of the radicalism that’s needed to keep up the fight for equality. But maybe the protesters who waved placards at Mr Buttigieg should think beyond the labels of queer, or hetero-normative, or upper class, or white, or middle of the road, and remember that gay people – all people – aren’t just fighting for the right to be different, they’re also fighting for the right to be the same.