I don't really know if there is damage done on either upshift or downshifting. I don't do full power clutchless upshifts, because I don't have the foot strength for it. I would have to let off the throttle so much, that it's easier and faster to just clutch it. I'll do no-clutch downshifts if I'm going lazy slow (I have the strength because pushing down is easy), but using the clutch lets me not worry about rpm and power that's going on, and I usually lock the brakes anyway.
Dirtbike or dualsport on pavement? Clutch always, end of story. Pavement has so much traction that you can easily wreck your whole drivetrain by being abusive on it. I say "can" because somebody out there has 20,000 slam-bang street miles on their 1997 RM125, and they will be posting here shortly to tell me I don't know boo-bop-beans.
No "foot strength" needed, shift it as you normally would without using the clutch...in my case anyways...
PS: Make sure to put on your flame suit for the 125 with 20000 "street" miles statement!