Heck one of our Catholic high schools shared a football stadium with the Lutheran high school. Also they had only one Lutheran parochial school so they played in the CYO leagues so they didn't have to play the government schools.
Years ago when we lived up north we lived in a very small village. There were about 6 different denominations. They formed an area association of churches. The purpose was to avoid duplication of effort. The AOG had purchased the old high school and took over the furniture ministry. The Larger Catholic Church took over the Clothing ministry. The Lutherans took over the food pantry. My wife worked there and was in charge of that. The Pastor was a woman and the secretary was Episcopalian converting to Catholicism.
None of the pastors had any difficulty sending people in need to any of the other churches to receive services. And none of them would have even thought about flock poaching.