Put yourself in the shoes of a woman in wartime Britain. Do you see that poster and think "Oh! I might volunteer!" or do you think "Urgh what a cruel race of people! Even their Red Cross workers are evil to the core". It doesn't once refer to recruitment when British propaganda about war bonds, recruitment etc was very direct.
The Germans had their own Red Cross in WW1. The writing said "Red Cross or Iron Cross?", suggesting that even as a German organization that aids people, it is inherently evil because it is German.
"No British woman would do it" is only there to contrast the morals of the two countries, to affirm Britain is good and Germany is bad. The answer is the Germans are inhumane.