The term "front" suggests control which was probably not the case. The republican Wolfe Tone clubs were very involved in setting up NICRA and it combined them with a variety of trade unionists, liberals and left wing activists. There were also a lot of local organisations with fewer republican connections.

Civil rights was part of the IRA's strategic shift from militarism to social activism in the 1960s.

There are two agendas who tend to overstate republican control of the civil rights movement. Modern Republicanism wants to claim ownership of it and modern Unionists prefer to use republican involvement to reduce its legitimacy. Therefore we have to be wary.

Sources:

Bob Purdie, Politics in the streets : the origins of the civil rights movement in Northern Ireland