Nativity School of Worcester needs to abide by the prescripts of Bishop Robert McManus

 Can. 806 §1. The diocesan bishop has the right to watch over and visit the Catholic schools in his territory, even those which members of religious institutes have founded or direct. He also issues prescripts which pertain to the general regulation of Catholic schools; these prescripts are valid also for schools which these religious direct, without prejudice, however, to their autonomy regarding the internal direction of their schools.

Apparently this truth has been forgotten by some.  As noted here, "A Worcester Jesuit middle school and the Diocese of Worcester are at odds over Black Lives Matter and gay pride flags flying on the school’s campus.

Diocese Bishop Robert J. McManus said the flags symbolize messages that conflict with Catholic teaching, and suggested the Nativity School of Worcester could risk losing its Catholic identity if administrators don’t take the flags down.

In response, the Nativity School said the flags are meant to show that all students 'do matter and deserve to be respected as Christian values teach us.' Although the school said it operates within the diocese, officials made the distinction that it’s not a diocesan school. The Nativity School is an accredited tuition-free, all-boys school mainly serving students of color from low-income communities.

School administrators said they’ve been flying the Black Lives Matter and gay pride flags since January 2021. School President Thomas McKenney declined to elaborate what the bishop's threat could mean for the school.

'The Black Lives Matter and Pride flags fly below the American flag at our school to remind our young men, their families and Nativity Worcester staff that all are welcome here and that they are valued and safe in this place,' the school said in a statement."

In Ontario, a group calling itself "Parents as First Educators" (a name which reflects solid Catholic teaching), circulated a petition titled “Lift high the Cross and not the Pride flag.”

In this petition. The group said that: "Parents exercise their choice when they send their children to Catholic schools, and they expect them to receive an education with Catholic moral teaching. Catholic schools need to be clear about the messages they give to children, and consistently teach students the truth about the faith,” the group said...Raising the Pride flag suggests approval of sexual activity of which the Catholic Church disapproves and violates Catholic teaching on chastity for all young people. Activists are using the Pride Flag motion to enforce their ideological agenda."

That's the problem in a nutshell. The Nativity School in Worcester doesn't have a leg to stand on.  Legally or morally.