The subway is a system for transit, not shelters — and it’s neither humane nor compassionate to pretend otherwise.

Progressives will cry foul, claiming Byford is heartlessly violating their rights. But no one has the right to sprawl on station benches, much less stretch out on a train. And New Yorkers on their way around town have every right to feel safe.

Byford told the MTA board he has no problem with people coming into the system to stay warm, “but lying across a seat or behaving in an antisocial manner or making a mess is not acceptable.”

Being merciful to the unfortunate, especially those with clear mental illness or substance-abuse problems, can’t mean the sacrifice of vital public space. Nor is Byford requiring transit cops to arrest anyone — just to enforce behavioral basics.

With Mayor Bill de Blasio and his allies sowing the seeds of disorder by effectively OK’ing public urination and pot-smoking, it’s heartening to see one public official drawing the line for public order.

It’s the mayor’s job to provide shelter for the city’s 62,000 homeless. Byford’s duty is to ensure clean, safe and pleasant conditions for more than 5 million straphangers a day.

They have rights, too.