It is true that generally, conservatives have tended to support more strict voting laws, but I'm actually not sure if I buy a fundamental psychological explanation for liberals voting more by mail specifically, since most research I can find suggests that states introducing mail-in voting didn't really make a significant difference in election results and turnout before 2020. It seems to me like the divide we see now is because of the specific context of Trump saying mail-in ballots were illegitimate and making it an explicitly partisan issue + liberals broadly taking the pandemic more seriously (making them more likely to pick the option that you can do from home).

This obviously isn't scientific research, but this is my partial theory for why in states where you can vote by mail up to election day (so long as it's postmarked), the late ballots tend to be better for Democrats. (Not saying this as an insult, I'm a pretty scattershot person with left-of-center views who tends to get my mail-in ballot in on the later end myself.)