Never done it to a snowboard but you may have to drill out the screws. If you've got a buddy with a drill press it's much easier than using a handheld drill.
If all else fails its the only way to take it apart without butchering the bindings and board.
Main thing is to get a good HSS bit just slightly thinner than the threads (use a screw that you've taken out or any standard binding screw as a guide)... If there are some threads left in the hole you can clean that out with a tap (i.e. from a tap and die set).
Now that I think about it if you don't already have these tools just take it to the board shop you bought it from! Which hacks did it, Mission or Source?
Shredlife has the best solution. Heat is the standard method for red loctite removal. This is super easy with metal parts, but you need to work carefully. Do as Shred said and heat the shaft of your screwdriver and keep as much metal to metal contact as possible. Use a small hand held propane torch and keep trying to break it free as you apply heat and be carefully not to overheat and take too much time.
I would also keep a can of water handy to cool the insert as soon as you get the screw out. Also, allow the board to completely cool before going on to the next screw.
Applying heat will damage both the binding and the snowboard around the inserts. Don't use heat. That's great for bolts on a car - but even on a car you don't use a torch if the bolt you are loosening is near rubber lines or wires or anything else that will be damaged by heat. By the time the nut expands with heat to loosen a touch, those wires or lines will be trashed.
The impact gun will take care of it, no heat required.
There were some good suggestions here for cutting a slot if required to use a flathead if the screwheads are too far gone. You might cut a bit into the binding disc, but probably will be OK in that respect as well.
Good luck - minimize collateral damage - don't use a torch.
What brand of binder is stuck to the board? Does it have a plastic disc that can be easily replaced with a simple email to customer service? If so then you can always cut apart the disc to allow full access to the stuck bolts. Then a simple pair of vise grips, with an extension for a little leverage, will solve the problem.
This way you avoid using a torch or an impact driver on the board, not so good for your board. If in fact the shop used loc-tite on your board NEVER LET THEM TOUCH YOUR BOARD AGAIN.
Just my 2 cents. The red loctite hypothesis is just an assumption.
All we know is that the OP stripped his screws. They could just be in their tight with blue loctite. Surely there are very few board shops stupid enough to use red loctite. Anyone knows for lots of different reasons bindings need to come off the board.
I would take it to a shop, preferably the shop that screwed them in so tight and get them to deal with it. At least get them to clarify if they did indeed do such a moronic thing as to use red loctite. Once we know what the situation is for sure, it will be easier to solve and might just be a simple job (if no red loctite is involved).
Hey guys this is also assuming that he used the right screw driver and didn't round them off because the wrong size screw driver head.
I"m constantly removing my bindings when I wax my board, another assumption since OP'er didn't say. I wonder if he ever loosened or removed his bindings the whole season. I'm guessing not since they are in there so good.
I also can't see a shop using red loctite but we all know not all shops are great.
To wolfs idea I would just point out that the OP'er had better make sure the torch tip is at minimal parallel to keep as much extra heat away from the board as possible. Maybe lay some wet towels around the top of the board to prevent heat wash and possible overheating of the board.
It may also be worth the $5-$15 to just take it to a shop, any shop and say I F'ed this up can you get these out. I'm sure they have seen this before.
We all had good ideas, depends really on the OP'ers skill level of using different tools. Everyone is trying to get him out of a jam he created.
Good luck and hope the outcome is positive.
I've done the heat thing to free stuck nuts and bolts many times.
One technique that I've used when I'm concerned about damaging the surrounding area is to use a soldering pencil. Plug it in, heat it up and prop it up on a piece of wood so that the tip is resting on the screw but the rest of the pencil is safely away. Let it sit for 15 minutes, take it away and melt an ice cube on the screw.
It may take a while for the screw to absorb enough heat, but I've never damaged the surrounding area