As a deacon and an avid disc golfer, I have a few points to make.
First, the issues being raised by those that have a problem with being approached while on the course are merely issues of perception and intent. I have talked with many people about God, Jesus, salvation, etc. I can tell from the first 2 exchanges of a conversation whether or not the person is receptive or shut-off. If someone is shut-off, that's the end of the conversation. If the person is not receptive, however, I don't just write them off as a heathen worshipper of Satan. I understand that people have the right to feel the way that they do and that's the end of the story. I am extremely offended by the use of the word "slimey". A christian that approaches you is not looking to gain something. Most could care less if ever came to their church. In their mind they are offering a gift that is more precious than anything in this world. A true Christian's love for mankind causes them to desire to share the free gift of salvation to all who will hear. You never know who will hear, until you ask. "Slimey" is a better term for playing a privately owned course, and while you are there, the owner comes up and tries to sell you a tent-time-share on their land for a flat rate. A christian that approaches someone about Jesus has nothing to gain from the conversation and they are doing it out of sincere love. Most people who are annoyed with this fail to see the true intent.
Secondly, if the church owns the property, you have the choice to play there or not. That's a personal decision. But I cannot for the life of me understand how someone would attend a tourney at a church-course and then be offended if a prayer was offered.
Lastly, those that are worried about being "preached to" need to find their own peace. I can listen to an atheist lecture and not be offended. While I might disagree, that's how the atheist believes and he is entitled to his freedom of thought. 99% of the time someone who is annoyed when approached about Jesus, is annoyed because they either a) had a negative prior experience with a church, or b) any sort of "preaching" causes a rousing of guilt. If you don't believe in Jesus, that's you're prerogative, but there is no need to diminish the efforts of others who actually see religion as a purpose for their life.