I agree that this is a difficult issue... As I tried to point out with my title, I don't care if a true transsexual uses the bathroom that they identify with; I'm ok with Caitlyn Jenner uses the women's restroom as I'm more assured that Caitlyn going there is using the facility for its intended use. At the same time, a person that just claims that they identify with a woman yet hasn't undergone hormone treatment nor surgery, I don't have that same assurance, and so I'd rather protect true women's privacy and not allow that man in for fear that the man is more of a sexual pervert trying to view women in compromising situations.
I guess what I have an issue with more are the laws that relate to this issue. The problem with laws like these is that they are "one size fits all". Whether the law allows people to use whatever bathroom they desire or a law that forces people to use the facility of the gender that they are born with, all businesses would have to comply regardless of its own code of ethics. In addition to the law enforcing some view of ethics that not everyone agrees with, these laws are also difficult to enforce. As paints illustrated, laws requiring people to use the bathroom of the person's innate sex would necessarily require some authority figure / monitor to validate birth certificates, etc. to ensure that people are using the correct bathroom, yet at the same time as Joseph Backholm mentioned in the article, "self-identity" is a person's own person feelings / beliefs that too has no way to distinguish those who wish to go to the bathroom in peace vs. some sick pervert that is setting up hidden cameras in the women's locker room.
I think the best approach is moderation in the laws... Firstly, don't make a law federal (ie no constitutional amendment one way or the other) but rather let the states choose how they wish to handle the situation themselves. When the whole country is required to follow a particular law, you take away more people's freedoms forcing more people to adopt some value that not all subscribe to. Also by keeping it at the state level, we can have states with very different viewpoints and so can do a better job of "experimenting" to find the best law. Secondly, allow businesses to decide how they wish to handle the situation. Let the "invisible hand" of the marketplace guide the businesses. If customers feel that a business that enforces gender-specific facilities is too harsh on transgendered people, then that business will lose sales and hence money. Conversely, if customers feel that allowing people to "self-identify" with the facility they wish to use takes away from their privacy, they'll turn to other businesses in the same market that does more to assure people of their privacy. The best policy for a business would be something that helps the most of their customers while minimizing loss of potential customers due to that policy. Thus I've already began to witness how many of the more recent buildings being erected nowadays don't have any gender-specific rooms, but rather more single-person rooms (eg "family" restrooms that have only one toilet and sink for use by one person at a time). These buildings offer customers the most in terms of privacy while at the same time minimizing transgendered people feeling marginalized by company policy. Yet even though I think that these type of buildings offer the best solution to the problem, I still would disagree with a law that forces all buildings to utilize only these types of facilities as the laws still don't know what challenges each business would face and again decreases the amount of freedom experienced by all.