I’ve been mounting brake calipers are they were stuck and not turning. I found the rotor(avid) was running into the caliper. I was able to get the brakes working without rubbing by using 2 lockwashers(5mm) between the brake caliber and the adapter. Is this safe to run any washer on this brake shimano mt200? If that is ok, flat washer would be better right? If that is unsafe what options do I have, change rotor, adapter?

i use non-lock washers for shimming the caliper away from rubbing on the discs, and also to move the pads away from contacting the disc spiders when engaged.....

Rotor with a more consistent diameter?

if your talking about 1 washer per hole between the adapter & caliper then you may have a 165mm rotor on a 160mm adapter.

Placing extra washers between the caliper and adapter moves the caliper away from the axle slightly, which will help if you have a wavey rotor that is topping out on the caliper.

those are Basic Avid rotors, and are not "too big".
the wavy circumference is to reduce squealing.
i have never seen a "165mm" rotor for bicycles, EVER.
there are 140, 160, 180, and 200mm rotors available, and i've seen a couple 203mm rotors too.... and there are some overkill 223mm rotors out there too...
the biggest things i see with caliper mounting errors are getting the adapter mounted in the correct orientation, and trying to use the wrong mount, entirely.

sidenote: RIM brakes on bikes are actually Really Large diameter DISC brakes.

I bought the brakes rotors and IS adapter as a kit from eBay, like $50. I have the IS adapters installed with top pointing up. I checked and the front is on the front and rear is on the rear. Maybe cheap IS adapter is the issue?

maybe.. or you just need a couple washers in the right places....
i always look for some clearance between the outer edge of the disc and the caliper slot where the pads are... i had brand new shimanos touching the shimano discs just two weeks ago.. a bit of fiddling got them in place and lined up.. meh... it's part of the job at hand,, IMO.
the bike frames/forks also vary a bit... "Manufacturing slop"

They stopped making those a long time ago I think?

Not really. One of the defining properties of disc brakes is that the rotor is mounted directly to the wheel hub. Disc brakes apply the braking force (torque) to the hub. And then it is transferred through the spokes to the contact area on the outer circumference of the wheel.

Kinematics of rim brakes is significantly different.

yes, the rim brake more directly applies stopping force to the tire and road surface, and reverses the braking load on the spokes.

they're still a larger disc brake.

And here are some "rim disc" brakes .

A 160mm Shimano rotor is all of $10. Stop d!ck!ng around.