I never connect my rear sway bar anymore. It's back there, but just dead weight with no end links. Even towing an enclosed trailer it is fine. If I were hauling 4 people with gear AND towing a trailer on the highway a lot, I might connect it.
I've run for weeks/months without the front swaybar on my sport trac and my old ranger. If you learn how to drive it you will be fine, just be smooth on streering inputs. I've cornered hard at 60+ and bottomed out one side, while the other is topped out, no problems, I was just smooth so the weight wasn't shifted fast.
And sure explorer are infamous for flipping, there are a ton of them out there, with wobbly passenger tires for stock. Plus most of them are driven by soccer moms who don't know how to properly react to unusual situations (ie driving off the shoulder and jerking the truck back to the road)...
A haven't disconnected the sway bars on my 4 door Explorer, never had it offroad. Although I did try to flex it in a ditch and it was PATHETIC.
Disconnecting them offroad makes a WORLD of difference. The suspension moves more freely resulting in a much smooth ride and better traction.