I would have thought American liberals (like me) would mostly view race as a social construct and therefore not immutable. However I am not an expert in sociology and my experience must be shaped by not being part of any visible minority.

I think that is true when considered in isolation at an intellectual level, but when any issue is discussed in more detail the assumption creeps through. Maybe because it is hard to internalise. Maybe because of the deep division: one thing very odd about the US is that black and white people from the same area (and whose ancestors have lived there for generations) speak different forms of English and/or have different accents.

For example, take the example I gave above. People will not accept self-identify of "race" and have their own ideas of what someone "really is". In America it is often based on the one drop laws of segregation: someone whose ancestry is predominately white can be considered "black".

Also, consider the term I mentioned, coined by liberal Americans. It embeds the racist assumption that the world is divided into white and non-white people: that everyone who is not white one group.