I have heard/used the term neo-liberal

But, you are correct, they are not liberal.

"My body, my choice" forget that you have to pay for it, and society has to suffer from a child raised without a father (majority of prison population, suicides, homeless...)

And the Marxist slant... what they want is complete state run support for their lives.
Others to pay for their lives. (but i have never seen one of these people actually get into farming... where they will end up if communism actually takes over)

(BTW, we will all be farmers soon.
You will grow your own food, in your own greenhouse, or starve
and half of it will be so that you know where the food came from)

I would probably describe myself as a liberal (back in the time of Reagan)
But that term has been hijacked by people who want the destruction of society
and the suffering of those who are productive.