Most sects of feminism are intersectional even if not explicitly stated. And feminists aren't an extreme group. Feminism, usually within communities of color, use intersectionality to describe different ways we're systemically oppressed. A queer latin transwomen will have different struggles than a straight white cis women. It's just common sense.
Learning new words are a part of life and the definitions of intersectionality and cisgender aren't difficult to learn. Saying a group is extreme because in your personal vocabulary you don't know words they do is mind boggling. I'm sure most people didn't know what Trans meant or pansexual but that doesn't mean they were an extreme group. And people eventually adjusted to using those terms.
And I'll just add, every trans person knows what cisgender means because that's part of realizing you're trans. It's like "okay I'm trans but what are people who're born with their gender matching their sex?? Cis. Okay they're cis." Obviously that's not how it goes but it's the best illustration I could come up with rn lol I'm tired.
Don't get me wrong. I educated myself and learned about these terms. But most people will not and I too felt that this was an unnessecary step and a complication. But in the end it is a sign of elitism to use a specialized vocabulary. If people don't understand you without learning a lot of stuff, you will not convince them about your point of view.
Using a special vocabulary works well in a small circle of 'initiated'. We as gamers use special terms specific to gamers. Like RPG, cut-scene, lag, aggro, party and so on. Using these terms in your circle is fine. But it fails the moment you try to communicate outside that circle. If you want that communication, you can't ask the others to learn your vocabulary. In politics you want to communicate outside of your circle. Because otherwise you lose, at least in democracies. You need to communicate to a lot of people and convince them, to get the change you want. That is why the usage of the specialized vocabulary is damning. Funny enough that left and right do it both.
Maybe extreme was the wrong word. I meant a group, that stands aside the mainstream. Extreme is often negatively associated, but you can use it neutral. But probably it is also not what I meant. I meant more a group that started to exclusively move in their own circles, therefore using the specialized vocabulary more and more as normal. That is what I understand if Jaicee references Jane Average. Sure enough even 'average' people are very differently. But there is a common core language that can be used to communicate with nearly everyone. If you want a change, you should use that. That doesn't mean that these words are per se bad, but you should be aware if the other side of your communication can understand these terms and their implications.
You should realize what using a specialized language makes with persons that not usually come into contact with these terms do. They feel excluded. Language can be used to separate the "Plebs" and the aristocracy. That can be intention or not, but normal person often understand a strong usage of many such terms as a separating language. Even if they understand the term, but it doesn't get into their day-to-day life a person making much use of such terms can come off as "the other one that doesn't understand a bit our life". Really, no way to convince people of the need of certain actions.
This is the same for right circles. "gynocentrism" as Jaicee said as an example is as much strange language as "cisgender". Use that terms sparsely and be ready to explain them if you communicate to the general public.