What puzzles me is this.
From the OP:
The mom has attended mega-church for a number of years, and shared that the church likes to keep kiddos together, whether it is sports teams, Sunday school classes, small groups, etc. This is great, as it's a huge church (20,000+), so it's nice that the kiddos can see a familiar face when they experience something new.
DH and I discussed, and ended up asking the recreation manager to keep DS7 on his current team. We explained that we recently moved, and DS7 was excited to know some people on his team. Rec manager replied that uniforms were ordered already and as good parents, we should encourage our child to make friends wherever he goes. DH responded, saying we would gladly pay for the extra fees to get one extra uniform, but, we really would prefer that DS7 stays on the current team. Rec manager said he could stay on the team.
Either the church has a policy of keeping kids together, or it doesn't.
I'd have responded to the email with something along the lines of, "We understood that the church likes to keep groups of children together, across sports, Sunday School, etc.? Is this not correct? What is the official church policy on this?"
Because if the mom is right, then the rec manager doesn't know the policy. Or maybe the mom has just observed kids being together and thought it was a church policy when it really isn't and the kids were just kept together by accident. But I'd want to know what the official church policy was, for future situations.
And yeah, the tone implied in "good parents would . . ." would really irritate me, as I see no other interpretation than the OP and her DH aren't good parents.
I think the OP handled the situation well. Her son is new to the area and new to the church--there were good reasons to ask to keep him on the team where he already knew some of the other players. As a military brat who moved every year for nine years, that little bit of familiarity would go a long way, and seems like a very reasonable request.