The 5.56 ammo is loaded to a higher pressure, but the pressure is well within the limits of any rifle.
The problem can be the chamber throat. The 5.56 has a fairly deep throat (to better accommodate the tracer round). This has the effect of reducing pressures in a rifle and also accommodates the seating of longer bullets in a bolt gun. A very nice feature if you shoot the 70 and 80 gr bullets.
The standard SAAMI 223 chamber has a fairly short throat. A 55 gr factory bullet is just barely off the lands. This has the effect of boosting pressures a bit. And can be a problem with military ammo, that may have a longer bullet.
But many gun makers put a deeper throat in the 223 faster twist barrels to better handle the longer, heavier bullets they can shoot. These rifles can shoot 5.56 all day long with no pressure problems.
I just finished testing 6 fairly new Savage 223 rifles. The blue barrelled ones had short throat SAAMI 223 chambers and the stainless barrels had a 223 with a deeper throat. I don't know if they now offer both or have switched over from on to the other.
When they introduced the 1:9 barrel (1:12 was the standard, at the time) they also included a SAAMI chamber with a NATO throat, so they could shoot 5.56. They may have stopped doing this.
Buy whatever rifles you like, and if they are short throated, it is a ten minute job to run a throating reamer into the chamber. I have done it many times.