Why does the American government allow known terrorists to work for them?

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I define a terrorist as anyone directly involved in terrorism and/or directly funds or supports terrorism.

I think most would agree but Rep. Peter King, a known supporter of terrorist murder and apologist of murder of civilians is an outspoken critic of terrorism.
Should he be removed from his position and barred from any government post of any sort?

How Peter King rationalized terrorism - Salon.com

Rep. Peter King, the Homeland Security committee chairman who will convene hearings Thursday on the threat of domestic terrorism and “radicalization” among American Muslims, is finding it difficult to shake his past. As is now well known thanks to a spurt of recent press, King was, as a Long Island politician on the make, an active supporter of the Irish Republican Army for many years.

Peter King, IRA supporter and enthusiastic counter-terrorism advocate

"The British government is a murder machine," King said. He described the IRA, which mastered the car bomb as an instrument of urban terror, as a "legitimate force." And he compared Gerry Adams, the leader of Sinn Fein, the IRA's political wing, to George Washington.

“The IRA’s violence is only a reaction to violence started by the British Government.”

But, Mr. King, the terrorist you condemn say they are reacting to violence caused by the American government.

King has also condoned murder of civilians so what the merry hell is he doing in the US government?

Surely you should support the Muslims' armed struggle and perhaps send them a few dollars.
Sort out a few parades where you could call Ossie Bin Liner a hero and compare him to George Washington.