My own personal thoughts are that he has reached the age of maturity and is feeling his feet. Its not unusual for Staffies at about 2 years old to start bullying.

I wouldn't muzzle him but I would keep him on the leash, sorry if this offends anyone but as soon as mine showed signs of not being friendly I used to yank him hard on the lead with a firm no. It disorientated him, if he could have talked he would have said wtf, but his focus had been diverted.

We progressed to the point where I used to make him stand off to the side and with the wait command giving the other owner lots of room to pass I always had a treat in my hand and he got the treat if he concentrated on me.

It was random with mine too, although I think if you look at the other dogs body posture you will find that the other dog is not comfortable with yours. Staffies wont stand for any non-sense.

Work with him, I'm not promising anything but its worth a try. My dog is now 3 and a half. I read his body language and yes I allow him off the leash with other dogs, I haven't made a bad judgement yet so far so good.

Good luck

Sue