@mikero First thought… keep an eye on your dog at all times when at the dog park. Stay close. Focus on him, not the other people. Not to say you can’t converse, but always have an eye on your dog. Be ready to jump in when it’s necessary.
My first Basenji, Jengo, was hot and cold. For the most part he avoided other dogs other than sniffing. Once he did, he left. Once in a while it would erupt into a scrap. Usually it was over quick, but there was one time I had to jump in and separate them. Jengo got bitten. The other owner was upset that I grabbed his dog, but so what. His dog was much more aggressive and I was afraid he’d continue to after Jengo if I picked him up. So, I grabbed his dog’s collar till he came over to control him.
I always have my guard up at dog parks. Things change fast and most owners are not paying attention. Also, by always watching your dog, you’ll get good at spotting their body language. You’ll know before he does that he’s about to snap. If you’re close enough you can call him off or grab him fast. Don’t stand in one spot. Follow your dog. He’s why you’re there. Not the other people. Basenjis don't back down. At least… that was my experience.