You are absolutely right. If you own a piece of property, or if the owner of a piece of property grants you control over it, you should have the right to restrict admittance or behavior on the property however you want. I support property rights just as much, if not more, than as I support free speech.
The problem then becomes, what if the message isn't being sent from your property? For instance, suppose someone across the street from the cemetary is holding a protest sign. How should the law address that situation...or should it even try?
Personally, I think it might be permissible to enact certain "place" restrictions on these protests. I could see a law requiring protesters to stay back far enough so that they could not drown out funeral services with their shouting. People at a funeral service can choose not to look at the protest signs, but they can't turn off their hearing, especially if they want to hear the eulogies. Such a restriction could be seen as protecting the cemetary owner's/renter's right to the enjoyment of their property, while still allowing the protesters to put out their message to the public and to those attending the funeral (on the way in and out). It would be the same as restrictions on "disturbing the peace" in a neighborhood.
Same principle as in the public park.
If I rent the pavillion for a family reunion and some yahoo comes along and starts megaphoning obscenities at me from a distance, then he is harrassing me and is not exercising anything except a violation of the air space that I had rented.
In renting that area, I have an expectation of control of the environment for that time and place....to include sound and scenery.