For all the jokes I see about feminists (and, frankly, anybody left-of-center) not having a sense of humor, I don't see much in the way of conservative humor. There's Anne Coulter, "Roseanne", Milo Yiannopoulos (I think), and...well, I'm not sure. A lot of it seems to not translate well, but when pressed, I've only been told I'm too stupid to understand it.
First off: you’re not stupid. They’re mean. If someone tells you you’re too stupid to understand something, they are a jerk and you have the right to ignore them.
Now that that’s out of the way….
Conservative humour is all about punching down and conformity. Like a lot of things that are part of conservative culture, it is very focused on keeping ingroup cohesion over most other values. Like, say, ‘kindness’ or ‘curiosity’.
So conservative ‘humour’ - what little I’ve seen of it; mostly National Review columnists who were trying to be Funny About The Disk Horse, minion memes, and crap from the alt-right really- is mostly about saying “we are not like these other people, you know, the shitty ones.”
People come together more easily when they have some shared dislike. A good example of this (...that’s not likely to be controversial on the hellsite) is Straight People Performatively Bitching About Their Spouses. The straight people who keep going “ach, [my spouse’s gender] must be a whole nother species, can you believe they [do gendered stereotypes] and [do things I don’t like]??” mostly don’t hate their spouse, but it’s a way to maintain ingroup cohesion with their other straight same-gendered friends. I’m a [gender], you’re a [gender]. Our spouses are not a [gender], therefore they’re weird and alien and not like us.
It keeps everyone in the ingroup close (because they dislike the same thing) and keeps people from the outgroup out (because they like or are the thing you dislike). I’m Like You, You’re Like Me. Those Other People, the ones who Do The Thing, they’re Not Like Us, so we’ll make fun of them. It’s a form of bonding, like monkeys picking flies off each other.
Conservative humour is making fun of liberal arts students who didn’t get a ‘real’ job, or Those People who sag their pants and talk funny, or people who are scared of guns, because they’re part of the outgroup, they’re Not Like Us. It’s making fun of “liberal hypocrisy” or a self-proclaimed feminist having a meltdown in public because liberals have to be crazy to believe the things they believe; they’re Not Like Us. It’s making fun of gay people and GNC people for doing gender “wrong”, because They’re Not Like Us. It’s making fun of literal fucking children for doing something ‘liberal’ their teacher or their parents roped them into, because They’re Not Like Us.
It’s being deliberately mean for the sake of mean- or in the case of the meme-y part of the alt-right, being deliberately gross for the sake of gross- to bring the group together and keep other people out.
Feminists and liberals “don’t have a sense of humour” because they’re not willing to indulge in the conservative kind of “funny” mean for the sake of mean. (Don’t get me wrong, there’s plenty of that on the lefty side of the fence- ‘male tears’, anyone?- but in general feminists are not fond of sexist/racist/homophobic humour, even if they’re normally part of what would otherwise be the conservative ingroup.) They’re willing to call that shit out, and usually the first thing they say is ‘that’s not funny’.
“Liberals have no sense of humour” is code for “liberals are part of the outgroup.” “They’re not willing to believe that making fun of people like them is funny, therefore they’re Not Like Us. And that means we’ll make fun of them even more for it.”