I'm hoping to run two 240 V 50 A outlets for an ARC welder. One will be outside and the other inside the shop. If I install a double pole double throw switch such that only one receptacle can be energized at a time, would the two receptacles be allowed by NEC to be on a single breaker in the load center?
When properly sized the breaker is sized to protect the conductors and will not allow you to overload them.
Consequently, you can put as many receptacles on a circuit as you want and if the circuit is overloaded the breaker will protect it.
You don't need a switch, especially if you only have one welder since you can't use more than one receptacle at a time anyway.
Just parallel the outlets and you are good.
Just to add some context here are some pertinent Code articles:
210.19(A)(2) Branch Circuits with More than One Receptacle. Conductors of branch circuits supplying more than one receptacle for cord-and-plug-connected portable loads shall have an ampacity of not less than the rating of the branch circuit.
210.21(B)(3) Receptacle Ratings. Where connected to a branch circuit supplying two or more receptacles or outlets, receptacle ratings shall conform to the values listed in Table 210.21(B)(3), or, where rated higher than 50 amperes, the receptacle rating shall not be less than the branch-circuit rating.
Exception No. 1: Receptacles installed exclusively for the use of one or more cord-and-plug-connected arc welders shall be permitted to have ampere ratings not less than the minimum branch-circuit conductor ampacity determined by 630.11(A) or (B) for arc welders.
This last one means if the welder has a duty cycle the circuit can be downsized.
Good luck and stay safe!
I would not recommend two welding receptacles say rated at 50-Amps on a single circuit made up of #8 wire on a 50-amp breaker. The breaker is not there to protect against stupid. The double throw switch would be one way to deal with the issue. However, given the cost of that type of thing I expect that a second circuit may cost less.