It's not the tube that's critical, it's the yoke. The horizontal deflection coil in particular is critical as it's part of a resonant tank circuit that includes the flyback transformer. This circuit has to be properly tuned or something will go bang. It's the reason multisync monitors were so much more complicated.
Generally speaking, most CRTs that have the same number of pins on the neck are more or less compatible electrically. It's rare for a yoke from one monitor to be close enough to work well in another model though. Sometimes you can swap the yoke, but doing the geometry and convergence alignment on a color monitor can be an exercise in frustration. Every adjustment interacts with every other.