If a sine wave filter was placed on the output of the VFD, it could filter out the rail-to-rail switching noise from the VFD output that might interfere with the sensitive parts of the equipment. There could be radiated and well as conducted interference. And so the VFD output conductors should be shielded or be in conduit. Ferrite chokes could be used to reduce the common-mode high frequency noise. I haven't priced sine wave filters, but they are not going to be cheap.
You might see if the equipment vendor can provide any information about any susceptibility of the equipment to interference, and if so, recommendations or guidelines that should be followed to alleviate it.
Will the vacuum pump motor be located very close to the more sensitive devices, perhaps even in the same enclosure? If the vacuum pump could be physically separated from the other parts of the instrument, that could help reduce coupled noise. Also, the VFD itself could be placed in a metal enclosure to shield it. If the VFD is powered by the same UPS as the rest of the instrument, then that could be another pathway for conducted noise that might need to be filtered out.
A soft starter has the advantage that it should not produce interference once the motor is started and it's in bypass mode. However, even though a soft starter reduces the RMS starting current, there may still be peak instantaneous currents that are quite high when the SCR's turn ON. It's possible the UPS might not handle that well unless it is sized sufficiently for such peak currents.