Quick tests for the material of the shown white RZM tag:
Flame test:
Cut away one of the threads you want to test, pick it up with forceps and burn it with a lighter.
If it has some plastic in it it will rather melt than purely burn.
If it smells like burnt plastic, this is another indicator.
Last but not least the flame on the thread might be rather green for a shot time.
You may burn a thread from a cotton piece first to be able to tell the difference.
Just take a thread from shirt or some Jeans (make sure it is 100% cotton) for that.
Black light test:
Many items produced after 1945 glow under "black light" UV light.
I use a small torch (flashlight) in a darkend room. It costs only about 10 Euro.
You will see that modern paper for example glows tremendously.
Old papers will not glow. The same goes for white fabric.
Both tests will only prove that an item is not old of it melts like plastic, or glows under black light.
If it does not glow and does just burns like normal cotton does, it will not prove anything.
Even today some companies still produce cotton that does not glow. Especially if it has not been whashed.
Washing with modern detergents may leed to a glow, because flouride and other components are used in modern washing powders to whiten the washed fabric even more. So, if an item has been washed with more than a traditional soap, it might now have a slight glow even if it has been original.