I've been shooting 308 with my Aero Precision M5 lower with a Rainier ultramatch  308 18" barreled upper with no problems however recently I've decided to purchase a 6.5 Creedmoor complete upper with a 22" 6.5 CM barrel and I've been wondering whether or not its a good Idea to use 2 uppers of different calibers with one lower or would it be advisable to have 2 separate rifles, each upper with its own lower receiver assembly.

Your prompt replies will be appreciated.

Works great
I originally did this with a aero precision receiver set, and Wilson combat 14.7 inch recon barrel(.308) and a ballistic advantage 22 inch fluted (6.5) worked well, however that  set up required that I also swap buffers.   so I changed the 308 barrel to a Ballistic Advantage  government 16”
No need to change out buffers with second set up.

In my opinion, you are going to want to have a dedicatedBCG for each upper.

There will be no issue with swapping, but if you are anything like me, you'll end up wanting a second lower.

I'm in the same boat with this guy, OP. I have 2 .308 M5 setups, one with a collapsible Magpul stock and and ALG ACT trigger with a 16" upper, and another that has a fixed Magpul stock and LanTac ECT1 flat-faced trigger with a 20" barrel. They both fill different roles when I feel like shooting .308 instead of 5.56

Thanks for all the replies. I know it seems elementary but I'm getting into precision shooting and I don't want any one factor to cause an issue with accuracy. I noticed that after fitting the 6.5 CM upper and tightening the tension screw on the Lower receiver  then going back to the 308 there is a slight amount of play between the upper and Lower receiver but I don't think that it will effect accuracy. Any thoughts on that?

I agree. I'm gonna get a second lower in a little bit.