Is it normal Allen keys are loose fitting? I notice on my chinese made Norco that the keys are very loose fitting.
I know there are different sets of allens but I seem to remember them either fitting snugly or not at all. The reason this concerns me is
it feels like I could strip the hole especially on the brakes which
have to be tightened down well.
They all have some play in the fit. The target outside dimensions for the most common bike hex wrench sizes (4, 5, and 6mm) are all around .1mm less than the bores they fit in, which match the nominal sizes with a tolerance of I think +/-0.05mm-ish. That shouldn't lead you to feel they're "very" loose, but they typically aren't exactly snug. Very loose suggests using imperial aka fractional/SAE wrenches, whereas virtually all Allen bolts on bikes are metric. The only exceptions I've encountered are certain 90s BMX stems.

That it's Chinese is here nor there.