Most people that consider themselves conservative, are not deep into the fundie zone. They tend to have a big continuum of personal interpretations and beliefs, that loosely aggregate under the christian dogma's views on sex. (Only between man and woman, only in marriage-- Otherwise just fine, but kept in private.)
It is when you get into fundie-ville that you get really scary off the wall shit.
The fundemental strawman is asserting that all conservatives are fundies. They are not.
However, the fundies are notoriously "Loud", and so get disproportionate representation in large public matters. (mainly because their over-the-top-ness makes the magnets for the press, which gives them exposure to spread their ideology, and when a group gets enough exposure, it starts to sway the whole demographic.
There's science on that kind of thing.) This is why they are the immediate boogey man of the extreme abortion-rights groups, (as you mention), and also appear prominently in topics like this.
I was pre-emptively bringing out that boogey man, outright declaring it a parody that is not truly indicative of the greater proportion of the demographic, and lamplighting this fact, to avoid it being used more seriously--
There was also an undercurrent of acknowledging that there really are batshit people who really do hold such views, and that they are in fact shaping public discourse, and so infecting otherwise sensible people with some level of their extreme ideology. (EG, since the original proposal tried to make it look like women's suffering was straight up at odds with the central dogma, I was being cheeky in pointing out that there is a very real misogynist bent to conservatism, and that the proposal fails to incorporate this, and so it will not get as wide an audience.)
It's a lot less funny when I have to break it down like that though. Explaining a crude joke always takes all the fun out of it.