If we want a national war over bathrooms, there is no better way to get it than the federal government telling every public school in the country it must allow students access to whatever facilities they want. Get ready: New federal guidance, released last Friday, does just that.

Much of this debate has been framed as conservatives versus liberals, or traditionalists versus social change. But the root problem is not differing views. It is government – especially federal – imposition.

Before getting into what the feds should or should not do, let’s be clear about something. A couple of weeks ago, U.S. Secretary of Education John King called “hateful” North Carolina’s law – ground zero for all this – requiring, among other provisions, that public school restrooms be restricted by a person’s sex at birth. Now, the law’s supporters may hate transgendered people. But many – perhaps all – may also harbor no such animosity. Neither Secretary King, nor anyone other than those people, knows.

It is not hard to imagine how perfectly decent people might be against opening up school bathrooms. Single-sex bathrooms and locker rooms have long been the norm, and privacy about our bodies – especially from the opposite sex – has long been coveted.

Beyond being unfair, King and others may be playing with social fire by branding as hateful all who oppose open bathrooms. They may be provoking anger from people who before were just concerned. And would supporters of the administration’s directive pronounce that President Obama was hateful until 2012, when he changed to support gay marriage? Probably not.

Of course, transgendered students should – must – be treated equally by public institutions, and their desire to use the facilities in which they feel comfortable is utterly understandable.

By fair reckoning, we do not have a competition between good and evil, but what should be equally protected values and rights.

How do we resolve this? Most immediately, not with a federal mandate.

Unlike most of the education governing Washington does – think No Child Left Behind – the feds may have constitutional authority to act here. At least Washington is empowered to prohibit discrimination by state and local governments under the Fourteenth Amendment, though the new directive is technically linked to federal funds.

But just because Washington may do something does not mean it should.

First, it is far from clear that single-gender bathroom rules are discrimination on par with, say, racial segregation. At the very least, it is difficult to argue that bathroom rules create unequal provision of education tantamount to completely separate schools.

There is also good reason to believe that it is most effective to allow social change to evolve from the ground up, not be imposed. Seismic change is jarring, and imposition may create otherwise avoidable resentment and anger. Moreover, changing attitudes may well precede – not be driven by – changes in law. For instance, white survey responses on racial integration show that in 1942 only 32 percent of respondents thought black and white children should go to the same schools. By 1956 half said so. By 1963 almost two-thirds did. The federal Civil Rights Act did not come until 1964.

So how, in public schools, do we treat people equally who have mutually exclusive values and desires?

We cannot. Open the bathrooms to all, and those who want single-sex facilities lose. Keep them closed, and transgender students lose.

The immediate ramification of this is that decisions should be made at state, and preferably local, levels. At least let differing communities have their own rules, which, notably, North Carolina’s law prevents.

That said, the long-term – and only true – solution is school choice. Attach money to students, give educators freedom to establish schools with their own rules and values, and let like-minded people freely associate. Impose on no one.

Alas, not only has the Obama administration issued its facilities directive, but it has repeatedly tried to kill the school-choice program in the District of Columbia, the one place where the feds actually have authority to govern education. Mr. Obama really seems to believe that one size should fit all.

That is wrong. We live in a pluralist society, and for that we should be eternally grateful. To keep that, and also be a free and equal society, people of different genders, values, etc., must be allowed to live as they see fit as long as they do not impose themselves on others. That is impossible if government imposes uniformity on all.

Neal McCluskey is the director of the Cato Institute’s Center for Educational Freedom and maintains Cato’s Public Schooling Battle Map.