You can use "against" when there is a tangible threat:

Mace allows people to protect themselves against assault.

And you can use "from" when there is a non-tangible threat:

Not caring can protect you from feeling embarrassed.

The relevant distinction is contained in the meanings for from and against:

against — in resistance to or defense from: "protection against burglars."

from — (used to indicate agent or instrumentality): "death from starvation."

Pragmatically, there is very little difference between the two prepositions and you can more or less use them interchangeably. That being said, patterns do exist.

Food protects one from starvation.

Food protects against starvation.

Note that "one" is used in (1). You could say "protects from starvation" but it isn't as common. Likewise, you could say "protects one against starvation" but it is also more uncommon.

You can use NGrams to check the most common prepositions for each:

This can give you a quick overview of which is used where. But, as I mentioned earlier, it isn't a major issue if you use the "wrong" one. The differences here are minute.