SS amps are OK with open loads (infinity ohms). Tube amps ARE NOT. Tube power amps have an output transformer, and the bias current from the tubes runs through the primary of the transformer. With no secondary load, this is a bad situation. Blown OT or tubes or power supply.
Modern SS amps almost always have short-circuit protection, and don't have output transformers (unless it's some esoteric thing). So the open- and short- circuit issues are not a problem. I wouldn't recommend short-circuiting it for fun.
A passive A/B switch with no load is a bad idea. I'd second the Radial recommendation. You need a load for the tube amp always. If you want it to be happy, and I think that you do.
Some other random thoughts:
* Parallel jacks are not the issue here. It's two amps running into an A/B, then out the A/B into one of the jacks of the cab. No one is suggesting shorting the outputs of the amps together. A OR B, not A AND B. Though some A/B switches have an AND function. That would be bad.
* If you have a passive A/B with two solid state amps, and the switch is break-before-make, then all is well. Make-before-break would possibly cause problems with poorly-protected amps.