Lots of 'theory talk' on forums...
I don't move round bales, but from my practical experience using pallet forks (48 inch wooden pallet loaded evenly), my L3301 CAN move ~2000 LB of material off the ground some inches. Around this amount of weight, the curl function loses steam, so you must plan for that (it wont curl while lifted).
Normal 'comfortable transport height' is less than ~2 feet and ~1500 LB is doable. It can unload and move a ~1000 LB skid from a ~4 feet high truck bed. Moving ~1000 LB is EASY, but lift starts to max out if you try lifting too high.
Again these numbers are for using pallet forks. I have been unable to put anything in the bucket that it can't lift to max height... the limitation is the amount of material the bucket can hold and not lift. It holds ~ 10 cubic feet completely heaped to top...or 8 cubic feet more realistically. The heaviest thing you could put in there is gravel, which is ~100 LB per cubic foot and then you're still around 800-1000 LB which is in the LA525 max lift height spec. Any type of soil or other material will be lighter.
With a backhoe for ballast and tires filled, it has the power and stability to move this weight on a slope less than 10 degrees, however at 15 degree+ I wouldn't feel comfortable...though at this type of steep slope I'm not too comfortable driving a tractor on it period.
The lift charts from the LA525 manual are posted in this thread. Those numbers include the ~350 LB bucket, which they assume is used (not pallet forks). If you're moving with a bale spear, I'm sure that weighs less than a bucket, but it will be further out than the specs.
The L2501 is basically same tractor with only slightly less pressure for reduced loader capacity.
In summary, with proper ballast, these tractors can move a ~1200 LB round bale no problem. They wont be able to lift it to max height though. I think people are looking at the loader spec and forgetting that it actually lifts more...the spec is for MAX height.
The talk of 'well if can do it, but is it safe' is silly. The loader was designed to match the capability of the tractor so if it can lift it, it is safe. If it can't lift it or you have a more powerful aftermarket loader (or mod it by increasing pressure), then it becomes unsafe. They key part is you HAVE to have ~800 LB rear ballast (pref + tires filled)... putting a 300 LB box blade in the back and using some ag tires wont work well.
Last point about any other 'is it safe talk,' is an L2501/3301/3901 weighs around ~4000 LB with loader and filled tires. Add at least around 1000 for subframe/backhoe or whatever you got on 3PT. That's a 5000 LB tractor and question is can move a 1200 LB object out front...physics of this says yes and question becomes more if the loader is designed to be capable of it. Kubota designed the loader to be capable well under the limit of the tractor once its ballasted (without ballast, it will easily overwhelm the tractor). So basically if the hydraulics run out of steam, it's not safe to move it. If hydraulics DONT run out of steam and you have proper ballast, its safe to move it.
L2501 is marketed as an entry to moving round bales. It's the smallest tractor in the lineup that can do it. What I see is often people with bigger equipment underestimate smaller tractors and are always surprised when they see what they are capable of. The L series is NOT a tiny subcompact tractor...and even those are capable of much more than people think.