I find the reasoning behind objecting to government agencies not endorsing religion curious, given such an endorsement is expressly constitutionally forbidden in the United States.

Any observer seeing a Christian flag flying from a city hall flagpole would receive the clear idea that the city government endorses Christianity. This is not permissible.

On the other hand, a rainbow flag flying from City Hall would send the clear idea that the city government endorses equal treatment for all people, endorses non-discrimination, and endorses treating people kindly. This is not an endorsement of religion, and in fact has nothing to do with religion. These ideas, which government agencies are constitutionally free to endorse, are in fact accepted by a super majority of people who live in the United States. There's no reason that flying a rainbow flag should even be controversial.