Learn English – reciprocally VS. mutually

Mutual and reciprocal can be easily confused in certain contexts. The clearest explanation I've found is from the Synonym Study section for Mutual on Dictionary.com.

Mutual, reciprocal agree in the idea of an exchange or balance between two or more persons or groups. Mutual indicates an exchange of a feeling, obligation, etc., between two or more people, or an interchange of some kind between persons or things: mutual esteem; in mutual agreement. Reciprocal indicates a relation in which one act, thing, feeling, etc., balances or is given in return for another: reciprocal promises or favors.

The main idea behind reciprocal is "if you do this, I will do that in return" and the main idea behind "mutual" is "we both are part of the exchange of something". We might give reciprocal gifts (I give you a gift because you gave me one) and have mutual feelings of good will (we both have a balance of good feelings toward each other).

In your example sentence:

“For example, in the early Middle Ages a Romance ethnic unity, in the absence of any political bond, linked nations of the most varied origins. Reciprocally, on the question of ethnic unity, we must first consult language. ”

Here, "Romance" refers to Romance languages. Earlier in the passage the author writes "In general, ethnic unity always suffices to explain linguistic community." So, if we want to discuss ethnic unity, we should in turn discuss language and if we want to discuss bonds of a common language, we should in turn discuss ethnicity. The reciprocal relationship is "if we do this, we should do that, and if we do that, we should do this".

Another example:

Because both countries were determined to reciprocate with greater force if they were attacked, their mutual destruction was inevitable once the first attack was launched.