could a rhyolitic magma melt a ferromagnesian mineral like olivine?
This is an excellent question.

What does happen when you drop a crystal of olivine into liquid rhyolite?

There are several answers which all depend on the exact composition of the olivine, how much magnesium is in the rhyolite, temperature, size of the olivine, how much olivine are you dropping into how much rhyolite, and more.

Let's take the most extreme case of dropping pure Mg olivine (forsterite) into pure felsic rhyolite (a feldspar–quartz liquid mixture). For argument's sake let's assume full thermodynamic equilibrium.

First, rhyolites can dissolve some amount of Mg. Not much. Maybe 1%, maybe 2%. If it's only a tiny bit of olivine, the olivine will dissolve as a liquid into the rhyolite (you might call it "melt", but that's not the correct term), making the rhyolite a bit more magnesian.

If you add a bit more olivine, you saturate the melt with Mg. This means that a certain magnesian mineral will form in equilibrium with the rhyolite liquid. This could be biotite, amphibole, a clinopyroxene, etc. But because our simple system has no water and no calcium, pure solid olivine sounds like a good choice.

However, forsterite is not stable in felsic systems. It will react according to the reaction:

$$\ce{Mg2SiO4 + SiO2 = 2MgSiO3}$$

This is the reaction of forsterite (Mg-olivine), reacting with quartz, to form enstatite (orthopyroxene). Therefore, your olivine doesn't melt. It converts to a different mineral: orthopyroxene!

This is well illustrated by the following phase diagram, coming from this website:


Some more related questions and answers:

Melting point of minerals

Why do felsic materials have lower melting points than mafic?