Safr, a ride-hailing company for women, is planning to open for business in Boston next month. By hiring only female drivers and picking up only female passengers, the new enterprise aims to serve women who don’t feel comfortable getting alone into a car with a male stranger. Here’s to Safr’s success — may the company encounter only happy customers.

More likely, it will encounter James J. Foster. Or someone just like him.

Foster was the Massachusetts patent lawyer who, in 1996, applied for membership in Healthworks, a tony women’s gym in the Back Bay. When he was turned down on the grounds that the facility was for women only, Foster did what any agitator with a law degree would do: He filed a lawsuit, accusing Healthworks of illegal sex discrimination. A state judge, Nonnie Burnes, ruled in his favor. The law banning discrimination in places of public accommodation, she held, overrode any concerns female club members might have about being ogled or embarrassed if forced to work out among men.

So Healthworks and other supporters of single-sex gyms appealed to the Legislature to change the public-accommodations law. Lawmakers swiftly complied, exempting fitness centers from the statute’s antidiscrimination provision. Similar bills were passed in other states. As a result, women-only gyms today are alive and well, a thriving sector of the $26 billion US health club industry.

Maybe ride-hailing companies catering to women will develop into a thriving sector of the ride-for-hire industry. But first they’ll have to get past the barriers imposed by state and local antidiscrimination laws. As a matter of common sense and customer peace of mind, the case for letting Safr operate freely is no less compelling than the case for Healthworks was. Alas, the women-driving-women startup lacks one valuable asset that Healthworks and similar clubs had: hundreds of thousands of existing members whom lawmakers were anxious to placate.

Safr isn’t alone in perceiving a niche market demand to fill. A comparable operation, See Jane Go, is up and running in California, and Shebah is preparing to launch in Australia this month.

For a while, a company called SheRides was going gangbusters in New York, drawing plenty of favorable news coverage. But legal pressure from equal-rights activists and regulators forced the company’s founders to spend tens of thousands of dollars in legal fees; now SheRides is in limbo, no longer available for download at the App Store. Maybe Safr and other startups can avoid that fate, but I wouldn’t bet on it.

Should the law ban private companies from discriminating on the basis of sex (or race, religion, ethnicity, etc.)? There is wide agreement that invidious discrimination fueled by bigotry is contemptible, and most Americans accept the authority of government to suppress such ugliness from the marketplace.

But discrimination that isn’t clearly rooted in bigotry should be left to the private sector to handle. Where is the virtue in using law to attack perfectly reasonable business ideas — like just-for-women car services or fitness clubs — for no better reason than the fact that they aren’t being offered to everyone? It is one thing to disallow supermarkets and motels from refusing to serve black customers. But how about a “black-hair” barbershop for black customers only? Or a dating service restricted to Latinos? Or a men-only drinking club? Or an ex-military boarding house that declines to rent to nonveterans?

In a free society, the presumption — absent overt, invidious bigotry — should always be in favor of allowing private parties to use their own property as they judge best. Markets and civil society, not Big Brother, should be the primary arbiter of what types of discrimination are intolerable. No one should object to a ride-hailing service just for women. What we should all object to is a legal system so obsessed with enforcing equal rights that it denies women the right to choose the ride that feels safest.

Jeff Jacoby is a columnist for The Boston Globe.