Seen a lot of this, and no unsafe conditions result, at least so far. It's one big reason I get asked to "Take a look" at someone's pump gun every year when they can't hit the right Zip Code with slugs. And it's not confined to 870s.
I'm assuming you're tightening the mag tube nut handtight. Sometimes, even on newer shotguns, this leaves enough play for the bbl to move a bit. Tighten by hand as much as possible, then using a padded set of channlelocks, tighten it ONE click,and check. This should remove the slop and leave the bbl immobilized.If it doesn't,seek the tender ministrations of a good 870 smith.However, haven't seen any yet this quick fix didn't cure.