While in general play between upper and lower should not affect accuracy, if the play is extreme it is possible. Imagine a gun with a half inch of play side to side and up and down...it would be very, very difficult to get consistent control of the recoil in that case and I think odds that the accuracy would suffer would be very high.
So while under NORMAL circumstances it should not be an issue, there is the possibility that ABNORMAL play might actually generate issues...accuracy, or possibly feed issues. I have not looked at an XCR for a couple of years so I can't remember the design well enough any more to know whether there could be potential feed issues from extreme U/L play.
Definitely not a normal issue, but I would be hesitant to say that it will definitely NOT be an issue.
It sounds like you have a fairly extreme example of RA quality control. Assuming you bought it new, I would probably contact the seller and ask them to have a look at it.
We're fortunate in Canada that many of the retailers are as responsible, or more responsible, than the manufacturers themselves. Depending on where you got it, they may well go to bat for you and get it sorted/replaced/etc if they look at it and agree that yes, this is excessive slop.