I personally agree with the OPs sentiments (girls shouldn't pee with boys), but it pays to be specific when we're talking about these issues. It's much more complicated than simply decreeing "all boys and girls may use the others' bathrooms". So it helps to understand the biological and social facets of the problem, first of all. I'm not disagreeing with you, OP, I'm simply illustrating the problem, from a scientist's perspective. Hear me out.
Biologically, there are only two human sexes: male, and female. These are not dictated necessarily by your genitals, but they are dictated necessarily by your chromosomes. If your sex chromosomes have two X's, you are a female. If your sex chromosomes have one X and one Y, you are a male. That is what "sex" is. It's your DNA. Every single person on this planet is born either with male DNA, or with female DNA.
In the womb, every human being starts off with female physical features, even those who have male DNA. At about week 6, if you have XY (male) chromosomes, the body releases male sex hormones (androgens) and so the feotus' begins to change from having female characteristics (a vagina, for instance) into the male form: a penis begins to form, along with testicles. If you have YY chromosomes (female) the male hormones are not released and the feotus remains as a female. This is how biological sex is determined.
However, in very rare cases, even if a feotus has XY chromosomes (male chromosomes), it is possible to have a condition called androgen insensitivity (the corollary to which is estrogen insensitivity), which means that the hormones that are released to change the physical features from female to male, in the womb, have no effect. Therefore, it is entirely possible (though exceptionally rare) for a person with male DNA, to be born with female physical characteristics (to have male chromosomes but be born with a vagina and all the rest of the female body). But even then, most of these people never know that they have male DNA, until they attempt to conceive a child of their own -- they're sterile. Most of these "girls" are totally unaware they have the condition for most of their lives. Anyway, so that's sex: it's your chromosomes, your DNA. But gender is something different.
Gender is not necessarily about the physical outward features. Gender is the social manifestation of the individual's sexual psychology. So, when we think of genders, we don't generally think of male and female, we think of "masculine" and "feminine". The personality characteristics which are masculine (of the masculine gender) are generally attributed to the male sex; those characteristics which are feminine (of the feminine gender) are generally attributed to the female sex.
Now, obviously, if you have a genuine MEDICAL condition which means that you have male DNA but female physical characteristics (or vice versa), it is acceptable for you to be able to choose which gender you would prefer to be, but this is by far and away, very unusual; it is a rare, rare exception. Therefore, it is crazy to make children "choose" their genders; transgenderism is a rare psychological condition, and transexualism is a rare physical condition. Why impose this choice on the vast majority of kids who in fact have neither of these conditions? It makes no sense. But that is exactly what feminists, transgender people and their respective colleagues are attempting to do. They're denying the intrinsic binary gender qualities of most of the human race, in favour of dogma that presupposes without any evidence that gender is entirely removed from physiology. And they are wrong to do so.
There is a very valid reason why most humans who have male chromosomes (men), who are born with male characteristics (penis and testicles), behave in typically "male" ways. The male hormones have been scientifically PROVEN to cause behaviors that are aggressive and reckless; they have also been proven to increase physical strength, and been linked with analytical reasoning. What behaviors do we usually associate with boys? Recklessness? Aggressiveness? Superior strength to girls? Better maths skills? While female hormones (progesterone and oestrogen), have been proven to illicit empathetic responses, increase emotionalism, increase relative reasoning and inhibit aggression. Which behaviours and characteristics do we usually associate with girls? Quicker emotional maturation? Nurturing behaviours? Decreased aggressiveness? Inferior physical strength? Therefore, boys generally act like boys, and girls generally act like girls. Neurobiochemistry.
What feminists are attempting to do is force upon people the idea that the minority exceptions to this are actually the majority, the norm; that gender is entirely a fabricated social construct; that typical "gendered" behaviours are nothing but the product of conditioning. This is a complete falsity on their part: typical gender personality characteristics are dictated moreso by genetics and hormonal physiology (and their relative neurological impacts), far more than by social learning.
In honesty -- these feminist "scholars" -- there isn't a scientific mind among them. Most feminist "scholars" have degrees in fields like English literature, feminist theory or women's studies. These are fields which are totally unrelated to genetics or biological anthropology. Leave this stuff to actual scientists.
So that's the scientific aspect. As for the social aspect, the question: so what do we do about all this? Well, if someone -- even a child -- with a genuine medical condition like transgsexualism or AIS (androgen insentivity syndrome) wishes to use a bathroom, it is best for them to use the bathroom which fits their genetic sex (at least until they have completed their procedures), or for schools and other institutions to simply create bathrooms which have room for only one person at a time (our homes have unisex bathrooms that work this way). But to get something straight: I really don't think the government are asking you to allow all boys to pee with all girls -- that's an exaggeration and an unfair representation. They're asking you to consider the possibility that people genuinely do have gender issues. Yes, I do see your point also: boys are boys, and girls are girls (most of the time). So, as for asking young school-kids what gender they would like to be, that's a no-no, especially from a genetic point of view. It's normal for boys to act like boys, it's normal for girls to act like girls, it's normal for them to use separate bathrooms to avoid sexual misconduct. But it's also acceptable and compassionate to understand this topic properly and to recognize that exceptions to traditional binary genders do genuinely exist. Yes, they are exceptions. Yes, they are real. Yes, they should be considered.
But there is absolutely no need to ask children which gender they would like to choose, because if a child truly feels uncomfortable with his or her own body, I am quite sure they will raise the problem. It pays to be nurturing, respecful, helpful and understanding regarding these things. Many medical conditions have stigmas around them -- a decade ago it was any form of mental illness, particularly schizophrenia -- nowadays it is transexualism. These kids really do exist, and many really do have genuine medical issues, and that's okay. At the same time, it is not okay to force children to accept a dogmatic mantra surrounding these issues -- one that has no bearing on the scientific realities.
Compassionate isn't the same as crazy. Transexual isn't the same as "pervert". Exceptions are not norms.