But it’s with a lower case “R”.

It refers to people who want to eliminate the monarchy, particularly in the UK:

I'm think about blogging on this, and I just wanted to confirm that my sense of you as a "small r" republican (wanting to abolish the monarchy) is accurate.

— Jack Dorsey Is Objectively Pro-Nazi (M.G. Saroff) (@40_Years) November 18, 2019

Indeed I do

— Craig Murray (@CraigMurrayOrg) November 18, 2019

Craig Murray is a republican, not a Republican.