I have an M&P 15-22 rimfire rifle and I am thinking about putting this scope on it so I would use the same scope as my regular AR-15.

Mark AR MOD 1 1.5-4x20mm
https://www.leupold.com/hunting-shooting/scopes/mark-ar-riflescopes/mark-ar-mod-1-1-5-4x20mm/

I realize that most rimfire scopes have a shorter factory set parallax distance (50 yds) compared to center fire rifle scopes.  I also believe that parallax is less of an issue on lower power scopes.  Thus, perhaps it's not an issue here?  I plan to shoot the 22 at 50 - 75 yards most of the time.

So do you think this scope would be OK for my rimfire rifle?  Any parallax experts who can provide information is appreciated.  Thanks!

I am not an expert but simply look through the scope at 50yards on a target and move your head around. Does the reticle move over the point of aim  more than you would  like, is the target sufficiently focused?

Many centerfire scopes with no parallax adjustment can actually be adjusted for rimfire 50 yard parallax.  Especially some Leupold models.  Here is one of my VX-2 2-7x centerfire scopes.  You remove the front outside section.  It does not break the internal seal.  Inside is another threaded section that is slotted.  You can screw it in and out to change parallax, like scopes with objective parallax adjustment.  When the reticle does not move on the target when you move your head at the distance you want it set for, you're set.  Screw the outside sleeve back on.  Done.

Haven't tried this with a Mark AR, but it appears similar in design.

This, but I'd add paying attention to focus as well. With good form and consistent cheek weld you probably won't notice reticle movement, but focus could bug you. My guess is it won't, but without looking you won't know.

Also, consider that plenty of hunting scopes are fixed and work fine. In other words, you can probably make it work. Just depends on what you want and what, if anything, bugs you.