The obvious workaround for this problem is to disable interrupts while you're changing the Stack Segment register, and then turn interrupts back on when you're done. This is the standard way to prevent interrupts from happening at a "bad time". The problem is that the 8086 (like most microprocessors) has a non-maskable interrupt (NMI), an interrupt for very important things that can't be disabled.
Although it's unclear whether the very first revisions of the 8088 (not 8086) with this bug ended up in IBM PCs, since that would be a few years before its introduction, the original PC and successors have the ability to disable NMI in the external logic via an I/O port.