I think it's important to acknowledge the reason why some churches or sects have a disdain for Freemasonry. In particular, Catholics frown upon the Craft, with a papal ban that has stood for over 250 years. Catholics have their own boys-only club, the Knights of Columbus, and want its members there instead of associated with Freemasonry, despite the many similarities between the two groups. It's more about money and control than anything else, two ideals that are at the core of every faith.
That is what it really boils down to, in my opinion: money and control. The church wants its members to remain loyal followers...sheep, that are part of a flock. Freemasonry not only takes up a man's time, but his donation dollars and participation in philanthropic causes as well. Officers in the line could better serve their church by becoming Deacons, Elders, or the like. In addition, Freemasonry can appear to be some kind of cult, and the Craft as a whole hasn't exactly done a good job over the years on the PR front to dispel that appearance.
The money and control issue rears its ugly head within the bowels of Freemasonry as well. How many men are lost to Blue Lodge when they begin to get involved in SR or YR or Shrine? While dues continue to be paid, the man himself is often lost, never to attend lodge again. I've seen this problem raised on these boards and elsewhere time and time again. I see no difference between that and the concerns of the church.