"for civil rights" is a prepositional phrase being used as a modifier - in this case an adjective describing activists. The object of the preposition in this question would be protest as feelings and activists are both nouns.
If you break the sentence down, it is easier to determine the answer.
The word some is the subject of the sentence and is an indefinite pronoun that is plural.
"activists for civil rights" modifies the pronoun and is used as an appositive defining some.
"registered" is the verb and action in the sentence.
"their" is a plural possessive pronoun and agrees with the subject - some activists - in number (plural)
"feelings' is a noun and the direct object as it receives the action of registered.
"by means" is a prepositional phrase used as an adverb as it describes how they registered. The object of the preposition by is the word means (a noun).
"of protest" is another prepositional phrase modifying the prepositional phrase "by means" and the object of the preposition of is the word protest (a noun).