Golf course changes ownership must new owner honor old membership contracts?

That depends on what you mean by "new owner."  If the "new owner" acquired the entity which owned the golf course, i.e. bought its stock, then that entity still exists, and must honor its contracts.  If the "new owner" merely bought the assets of the original entity, then it probably depends on whether, as part of the transaction, it also assumed the original owner's obligations under the membership agreements.  If it did not, then it probably isn't obligated (there are some exceptions, but too remote to go into here), but the original owner would remain obligated and may be liable for damages incurred due to any breach.