According to Boston, raising the flag with a cross on it could be a violation of the First Amendment; which prohibits the government from endorsing a religion.

The United States Supreme Court found that the city of Boston violated a Christian group’s free expression rights; by refusing to fly a flag depicting a cross at City Hall as part of a programme that allowed private groups to utilise the flagpole while having activities in the plaza below.

The 9-0 judgement, authored by liberal Justice Stephen Breyer (PDF); overruled a lower court’s ruling that the rejection of Camp Constitution and its director Harold Shurtleff did not violate their First Amendment rights to freedom of speech. In this case, President Joe Biden’s administration backed Camp Constitution.
The flag-raising initiative in Boston was intended to promote diversity and tolerance among the city’s various communities. Boston had turned down Camp Constitution; because raising the cross flag may appear to be a violation of another provision of the First Amendment that prohibits the government from endorsing a specific religion.