Is the electorate required to adhere to the popular vote?
"In states where the electorate is not bound by law to follow the popular vote, do the voters have any legal recourse in, for example, civil court or even federal court, to protest the electorate not following the popular vote?"
The short answer is no, but it would create an epic shit storm of anger. Furthermore, you can bet that should an electorate not follow the popular vote, legal action would ensue and laws most likely amended in that particular state.
The long answer...
There is no Constitutional provision or Federal law that requires Electors to vote according to the results of the popular vote in their States. Some States, however, REQUIRE Electors to cast their votes according to the popular vote. These pledges fall into two categories: Electors bound by State law and those bound by pledges to political parties.
The U.S. Supreme Court has held that the Constitution does not require that Electors be completely free to act as they choose and therefore, political parties may extract pledges from electors to vote for the parties’ nominees. Some State laws provide that so-called "faithless Electors"; may be subject to fines or may be disqualified for casting an invalid vote and be replaced by a substitute elector. The Supreme Court has not specifically ruled on the question of whether pledges and penalties for failure to vote as pledged may be enforced under the Constitution. No Elector has ever been prosecuted for failing to vote as pledged.
Today, it is rare for Electors to disregard the popular vote by casting their electoral vote for someone other than their party’s candidate. Electors generally hold a leadership position in their party or were chosen to recognize years of loyal service to the party. Throughout our history as a nation, more than 99 percent of Electors have voted as pledged.
For more information on which states do and do not have electorate laws: