Why does my GCFI plug trip when I connect the ground?
First, you have to unplug everything plugged into any of the rest of the circuit downline.  It's pretty dumb to chase a wiring problem when in fact the problem is a plug-in appliance that would trip if plugged into the bathroom GFCI. 

Now most likely you will have cleared the trip.  If you're going "wait a minute, this has to work with that appliance plugged in, because my house needs that", then fix the appliance.  Or if it's a fridge or freezer, it should not be on GFCI in the first place, and you need to rethink your wiring strategy.  

Hook up ground first

You're getting blindsided by the fact that you hooked up ground last, as an afterthought.   "Correllation is not causality", but you get fooled into thinking ground had anything to do with the problem. 

So now, you need to connect ground, and go to about the halfway mark in your circuit's length, and open up the junction box there and see what's inside.  Disconnect hot and neutral so the downline is no longer on the circuit, power back up and see the GFCI trips.  


if it no longer trips, the problem is between here and the end of circuit.  
If it still trips, the problem is is between here and the GFCI.  


The rest can be excluded as positively good.  Reconnect what you disconnected. You still have a problem area. Go to the middle of that, find the nearest junction box, and disconnect hot and neutral as done here.   Continue divinding and conquering until you narrow it down.  

Divinding. LOL, a typo, but not entirely.  

Always keep all grounds connected.  When you see other defects, fix them.  However, switching hot and neutral on a receptacle will not trip a GFCI.  It might make an appliance trip a GFCI if the appliance is marginal.