I think most shops will look at the load rating more than XL versus SL. As long as the load rating is adequate a SL tire should perform safely on the road. Of course, if you venture off-road or drive really fast, there are other considerations. I am not sure I have seen Land Rover specify XL anywhere, other than most of the OEM tires seem to have been XL rated.
It gets a bit complicated, as one reason for XL tires is to gain a certain load capacity within a smaller tire. Obviously, as tires get larger, their inherent load capacity goes up. That is why many larger than stock SL tires you might use on an LR3/LR4 will have sufficent load capacity. Also, the speed rating of the OEM tires are generally higher than you will find on all-terrain tires. The higher speed rating is a function of tire construction and its capacity for heat dissipation, which is separate from actually being XL or SL. XL and SL construction differences are strictly for load rating. Speed rating, lateral stability, traction, etc are all controlled by other factors (such as compounds, thickness in certain parts of the tire, etc.). This is coming from a tire engineer, not me.
You'll notice the 2016 OEM specs below show a 109 load rating for the 20" wheels, but 111 for the 19" wheels. This is because there is simply more air capacity in the 19" tire. But, the lower load rating of the 20" tire has a higher speed rating, which is not by accident. I am not aware of how the actual wheels themselves impact the needed load rating of tires, or if they have any impact at all.
Load/speed index Front pressures psi (bar/kPa) Rear pressures psi (bar/kPa)
255/55 R19 111V 36 (2.5/250) 42 (2.9/290)
255/50 R20 109Y 36 (2.5/250) 42 (2.9/290)
The 19" version of the Adventure tire is rated at 109, which is on the low side, especially if you factor in the lower T speed rating. Combine that with packing up that roof rack with gear and possibly hauling a bunch of people too and it could become questionable under certain cirumstances. The 18" version is an identical 31" tire but has a 111 load rating simply because there is more air capacity. Therefore, the 18" version might actually work a little better for anyone running smaller wheels.
The bottom line is that as the wheels get larger, the tires will have less air capacity, and will therefore need more reinforcements to attain similar specs to larger tires on smaller wheels. This is where the XL/SL and speed ratings come into play. There is not one perfect answer as to what is acceptable, it comes down to what you do with your vehicle. When in doubt, follow the OEM original specs or exceed them and you should will be fine.