In practice LessWrongers invoke directly or implicitly moral progress all the time. Like this.

They also sometimes invoke "well people changed their opinions in the past on case A, B and C, surely we will change our minds on D too!". Taking the idea of moral progress seriously, its perfectly fine to say that no thank you but you'd prefer not to change your vales to pattern match arbitrary historical processes (and further more a potentially flawed pattern match of historical processes!), so you are not changing your opinion on D.

This is even true for people who happen to disagree with modern stances on A, B or C. Preserving one's values is most likley a prerequisite for maximising expected utility. In this sense all of human history has been a horrible tragedy with the vast majority of people (including people alive today), being born in a uncaring universe with a practical guarantee of an alien valueless future.