Should transgenders be allowed to use public washrooms of the gender they identify as?

Well I guess it’s strange to go in either toilet if a man is dressed as a woman at the time. This sounds odd I know but If he is just dressed in pink in a ladies cardigan then I would say he has to use the men’s since he is only particially dressed and he is still identical as a man. On the other hand some transgenders are very feminine and very good at what they do dressed as a woman so then I think they should be allowed to use the ladies facilities especially since the ladies are all individual toilets and showers etc.