In my .308 I normally load 168gr bullets and that is what my rifle is sighted for at 100 yards. When I shoot some cheap 150gr or 180gr bullets just to foul the barrel, my shots aren't even on the target backer. I would say I'm off by about 12-18" high and 12-18" left. Is this just because of the different bullet profile and weight or is there something else going on? I would normally see an impact shift in my .223 or 7mm rem mag, but only maybe 2-3" at 100 yards. This is very frustrating when I am testing several loads with different bullets.

Every rifle is a law unto itself. I have a .300 WinMag that will put my 180 grain load 6" higher than my 200 grain load. It is what it is.

That is unusual unless it's maybe some really light loads.

Shooting different styles of the same weight of bullet will have very different poi changes also.

So basically just sight in with the same bullet as my hand loads I'm testing

w2hat rifle is it?

Mossberg patriot action with a Boyd's pro varmint stock

This has been my experience as well; although I notice it less with a heavy contour barrel.

Correct!