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It wouldn't, golf is as likely to spread to multiple planets as are orangutans to achieve universal peace.
Every planet would have its own culture + Part of the culture of the colonizers, and It's very unlikely they all are going to be colonized by golf lovers, also with less gravity a lot of new games are sure to show up, with different environments, technologies who knows ?
Also, this question isn't about world building, it's about golfing in low gravity, so it would be better in the physics community rather than here, if any mod sees this close it please.

Most likely golf's influence is going to be narrow, and possibly contained in one plannet where it is part of their culture.
If that one planet where golf is a culture manages to colonize the other then there is a pertinent question on that which would be, its not golf anymore its a variant of golf.
Also, this question isn't about world building, it's about golfing in low gravity, so it would be better in the physics community rather than here, if any mod sees this close it please.