You have worn sight parts.
One common reason for loose apertures is a worn sight cover. That's the wide steel cover that fits over the receiver sight area.
This is actually a spring that tensions the sight aperture. If it's worn, the aperture will be loose.
Also, the rear sight base can be worn and the aperture itself can be worn allowing side to side movement. The rear sight base is the block the aperture slides down into.
SOME movement is normal on a GI rifle. Match grade rifles have all looseness in the sights tightened up by fitting and lapping the components.
Bottom line, you have worn sight parts, which is normal on most CMP rifles.
The "fix" is to either replace the sight components with new GI (not used) parts, in which there will still be at least some looseness, OR have the sight Match conditioned by an experienced builder.
FIRST, I'd talk to the CMP. It's very possible they will send you better components to replace yours with.