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

Yes. There is a want by society (the elite anyway) to allow the freedom to select your gender. However, regardless it would not be enforceable which bathroom they go into (would be hard to tell). So yes, allow them the choice. I do not agree with a "third" bathroom for those who do not know what they are. That is an expense to society that punishes the collective far too much for individual wants.