Why would a 150 MHz probe work fine for a 100 MHz oscilloscope?
That is right. Not a problem in doing that. Think of it as a filter between your oscilloscope and the point you are probing.

The bandwidth of the oscilloscope will determine the overall bandwidth of your "measuring system", since it is the most restrictive one.

For instance, if you are using a 150MHz probe with a 100MHz Oscilloscope, then the probe will attenuate the signals over 150MHz, and that input (with a 150MHz bandwidth) will enter your oscilloscope, which will then attenuate the signals over 100MHz. So your probe will pass the signals between 100MHz and 150MHz, but they will be filtered out by the oscilloscope input circuitry.
In the end, you will have filtered the signals over 100MHz anyway, so no big diference with using a 100MHz probe.

In the other hand, if you use a probe with lower bandwidth, then it will determine the bandwidth of your input filter, and you will have less bandwidth in your input filter.