I've ridden the entire trail a couple of times and the section from Sale to Southport lots of times solo. My wife and I have ridden the Warrington to Southport section and back on a tandem a couple of times. From Sale onwards the gates really aren't a problem. I don't remember getting stuck in any of them with the tandem. The real problem is at Widnes where there are some terrible steps with barriers down each leg. It truly is a horrible thing to put on a cycle route. Even solo it's difficult but taking the tandem down them and even worse back up them fully laden is seriously difficult.
Most of the gates can either be ridden through slowly or navigated with a quick dismount. Even though they are a pain, don't let them put you off, the section of track through Liverpool really is quite lovely in places.