Hi Martin,
It is very hard to tell on a B&W photo, if something is white or beige, with determine colors it's even worse.
My main hobby is scratch building pre WW2 slot race cars, and often you will be deceived with B&W photos.
To give you an example of this Gilmore Indy car.
If you look at the B&W photo, you could sware that the car is white.

Unfortunaly I can't find strait away a color picture of the same car, but
Gilmore is a American petrol brand and this licht beige is there house color.

This principle counts for everything, aircraft, uniforms etc..
The best way to be sure you have the right color is to hope it still exist today, and even then you have to be careful,color can be changed in restoration, or faded by time.
As for these type of coton tents out of the WW1 they where slightly beige, believe me.
That's why I adviced coffee thined with water.
You only must experiment a bit to get the right beige shade.
This is at least what I would do, the rest is up to you.
Cheers,
Danny