“Liberty, understood by materialists as the right to do or not to do anything not directly injurious to others, we understand as the faculty of choosing, among the various modes of fulfilling duty, those most in harmony with our own tendencies.”

The quote starts with a broken string of partial accuracies. At nature's law, liberty is what it "IS", no matter who's understanding. Fulfilling duty may be an action within liberty's domain BUT, it is not any part of liberty's definition. As to "most in harmony with our own tendencies", liberty is an innate faculty of birth in each and every / any and all of the family man (nationality, duty or personal tendencies do not play a role in liberty's definition or understanding).

I think Mazzini is saying that while 'materialists' define liberty as the right to do or not do anything that is not directly injurious to others, he understands liberty as the faculty of choosing according to conscience.  Makes sense to me.