The cities of Boston and Cambridge are suing the federal government over the potential loss of millions of dollars in funding for homelessness programs.

The lawsuit, which also includes other jurisdictions and nonprofits around the country as plaintiffs, alleges that changes to the funding criteria for the U.S. Department of Housing and Urban Development’s Continuum of Care program are illegal and will result in thousands of people going back into homelessness.

The changes include barring provider organizations from acknowledging transgender individuals, drastically cutting the amount of funds that can go to permanent housing programs and only disbursing funds to programs in states and cities that follow certain public safety policies.

“Boston’s Continuum of Care funds the backbone of o

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