I agree, we need to look at the costs of a policy and make the unhappy decision of deciding how many additional assaults / rapes are OK.
If we try to make rational public policy we can assign a value to life, to suffering etc. This is already done by policy makers - its well known that certain money expenditures can make predictable reductions in death rates(through improved emergency response). - so any time money is spent it is trading lives for something else. A typical value for human life is in the $10M range.
We have to be VERY careful though. Value of life doesn't mean that we want breeding farms to produce as much human life as possible. Cost of death doesn't mean that we want to kill every human on the planet so that the number of deaths in the long term is reduced. Its easy to get trapped by false optimizations.
All that said, how to balance trans, gay, racial etc rights against costs?
There is direct physical risk. I don't know if there are any statistics on the rate of sexual assaults by trans persons relative to the average population. If we then look for assaults by trans persons using facilities not of their birth gender there is probably even less data. My guess is that assaults by trans persons will be no larger than assaults by college athletes (both relative to the average population), and we tolerate college athletics. I have no number though to support or oppose this.
The benefits to trans people are pretty high because acceptance is important to them.
The cost of discomfort is more difficult. How many people are we willing to make uncomfortable in order to make some number of people happier? Is someone's discomfort at seeing a trans person the same as a trans person's discomfort at not being accepted? Or are they fundamentally different? I have no way to measure this. Hmm. tricky.
I'm all for rational policy, but sometimes things cannot be represented by numbers. So instead I'll take a sort of big picture look. When I look at societies that are accepting of a wide range of (non-harmful) behaviors relative to those that do not accept these behaviors, I personally much prefer the accepting ones.
My largest objection to many Islamic countries is that they so greatly restrict behavior: specific dress for women, no drinking, no extra-marital sex. Especially important is the extremely limited rights for women, generally argued as being required for "moral" reasons.
I would much prefer to live in a country that allows an uncomfortably wide range of behaviors than one that overly limits behaviors.
I am willing to accept gays, trans people, fundamentalist Christians and Muslims, Vegans, radical feminists, hunters, snowflake liberals, drunken frat boys, survivalists, neo-Nazis (non violent), gun collectors, etc - all of whose behavior makes me uncomfortable in some ways, in return for being allowed to behave the way I want, even though it makes other people uncomfortable.
Also, on the shower issue... would you say that public policy should serve the public? So if we are talking about either A) forcing people to let this happen to their kids or B) forcing them to not let it happen, would it be fair to say that the policy should be based on serving the public? Is the public better served by forcing A) or B)?
If we force A), how many rapes/sexual assaults would be necessary as a result in a given year, to display that it was not worth the gain in comfort for <1% of the population? How much discomfort should the remaining >99% of the population have to suffer for the comfort of that <1%?
These seem like legitimate questions, you being a utilitarian and all.