If I want to ask someone about their handwashing routine, is there any difference between
"Do you wash your hands regularly?" or "Have you been washing your hands regularly?" or are both possible?
Both are possible. Obviously the second refers to the person's habit until the present moment, but in practice both questions mean the same.
Do you wash your hands regularly?
is a more idiomatic way to ask it.
Have you been washing your hands regularly?
doesn't mention any period of time, which makes it a little unnatural, and I would say incorrect.
Have you been washing your hands regularly since that deadly virus came around?
Have you been washing your hands regularly since Covid-19?