I only let my terrier approach on lead because we have had problems with aggression in the past. He is far better now but still struggles with introducing himself calmly.
We have gone from one extreme to the other. All dogs no longer need to be eaten on sight before they eat him, they need to be dry humped into oblivion before they dry hump him
This can cause more timid dogs to snap at him in fear, after which he goes back to wanting to eat them.
I allow calm introductions on the lead but the minute he attempts his dry humping he is led away until he can calm himself down.
There are a couple of dogs I will let him play with because we know them well and I know they will correct his dry humping in a manner which he finds acceptable so we don't end up in scraps. These are dogs we mainly meet at the beach. Everyone in the park thinks I am an over protective owner who doesn't like my dogs to play with other dogs (nope, there are just far less numpties at the beach and far more people who are happy to help me train my errant terrier)
What really annoys me is when large groups of off lead dogs are allowed to approach my on lead dogs when I am clearly pulling mine to then side of the path and attempting to keep their attentions on me and me only. This tends to happen most at the local outdoors center where dogs are meant to be on lead anyhow 
Generally larger dogs are better playmates for my troublesome terrier, they tend to be calmer and more likely to tolerate his bad manners.
Whippy will play with anything bar small, white dogs who she tries to avoid after being attacked by a JRT once. She is fast enough to avoid any dogs who want to cause trouble anyway. Again I generally find bigger dogs to be more gentle playmates for her. Smaller ones can get a bit rough for her.