Ahaha, this was of particular importance to me, though my gaming is all pre-WWII (I'm working with a date range of 1934-1938).
COPPLESTONE:
Most (probably all) of the male civilians/bandits/gangsters/mercenaries are fine and some of the female civilians. The women gangster civilians are pretty clearly 20's, but you can bodge that as long as you don't mind that they're wearing cloches. The American beat cops are more clearly 20's/30's, but I think you could get away with using them through the 40's ok (some American PDs moved away from the double-button-row uniform, but lots hadn't).
The military uniforms are dicier. The Chinese might be okay? I'm not too sure there but warlords had varying resources, so I'm sure even if they're be out of date by the 40's you can justify it really easily. The Germans are clearly colonial to WWI and Turks are clearly WWI. The British forces are actually fine until the late 30's as the British WWII uniform update was very late (especially officers), almost right before the war (except for the sailors in the Darkest Africa range, which are clearly colonial).
The White Russians are obviously out, being BoB-only, unless you use them for some sort of made-up warlord/minor power soldiers (which you could!). The Red Russians are really BoB, but can be used up to the mid-to-late-30's with minimal conversion unless you're a weapons purist: The main physical changes from the BoB-era infantry to the mid-30's was a switch to side caps instead of peaked caps for enlisted men and the collar changed from being straight up to folded down. What I did was buy some heads with WWII Russian side caps and converted some of my infantry (I left my non-coms and technical guys in the old Russian peaked cap, even though they probably would have side caps too) and I didn't bother converting the collars. Then I painted everything in mid-30's colours with mid-30's trim/insignia/piping. Russian uniforms and systems of military address changed several times through out the 30's and again multiple times through WWII, so it's impossible to get figures that will last the whole period.
The natives/other tribal or local people should be alright.
STATUESQUE:
The Pulp and Asylum lines are fine. The commando/freedom fighters girls are more clearly Cold War.