It is supposed to be very snug to tight...define "a little play".. we talking a few thousandths of an inch or 1/8 inch? Is the spring present in the stock that puts pressure on the trigger guard?
It can affect accuracy, usually it will be very inconsistent with the action moving around, if real loose in a worse case, it can even damage the stock. You can shim it, see the photo below. Note the material between the rear of the receiver and stock, this is a worse case. It took 3 pieces of a cut up credit card to tighten the action in the stock, and notice the stock split from being fired while loose. As I said, this is a worse case, it had back and forth and up and down play, this is an Albanian I picked up years ago. This stock is now just for appearance, when and if I ever shoot it, I just move it to a spike bayonet Chinese stock I fitted to it. No one really notices the difference.
I would try shimming in the same area using something similar and thinner as needed, something that wont compress or just distort, like thin sheet plastic, brass sheet stock or even shims made from beer cans can work. This should hopefully put more force back on to the crossbolt where it should be. You would want to shim it thick enough to lock both together very firmly, but just with enough clearance to latch the trigger back in with a good amount of force during assembly. Another option, just to throw it out there, you could try a different stock, just to shoot with like I did, any blade bayonet Chinese or a Romanian would fit, a Yugoslavian would fit as well. This leaves the original stock unaltered and it wouldn't be damaged "if" something happened.

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