I certainly think they should.
I'll leave the "but that's just your opinion tho" quip open for our resident opinion-haver.

They are elected by "the people". What's the point in having a representative democracy if the government doesn't make laws which represent what "the people" want.
Right. But we have the mechanism for this. It's voting. If the elected state governments do not represent what the people in these states want, they should get booted. I think it would be very difficult, if not impossible, to expect elected officials to create policy against their conscience - if they are as massively at odds with the electorate as you claim, they shouldn't be elected in the first place.
So, by my intuition, something in the picture you drew makes it fall apart. My guess would be that most state legislators don't actually thump Bibles on the table while incoherently babbling about Baby Jesus (I'm sure
some do). It's probably more nuanced than that.
This seems like a particularly poor system, they're placed by the incumbent president and are there till they die, right? So a president who happens to be in when a certain number of them die can back the SCOTUS with people who reflect his (or her!) own views and they're there till they die, or become incapacitated, no matter how public opinion shifts in the meantime.
Not as bad as hereditary Lords, but yes. That said, in this case the decision is whether or not states should be prohibited from passing certain laws. Revoking this prohibition doesn't, by itself, impose anything on anyone. The reason people are twitchy about it is that they want to impose their own views onto everyone for much longer than anyone's lifetime.