In this period of frenetic ins and outs, it isn't merely the displaced political appointees who get caught in the draft from Washington's swinging door.

Consider the case of Allan Cohen. Cohen is an educator, now employed as a Washington-based official at of the Illinois Education Department.

But some members of President Reagan's staff knows Cohen better as the former chairman of an ad hoc committee for the creation of the Department of Education -- which the president has said he will dismantle -- and when he seen last week in the transition office of Terrel H. Bell, the president's choice to head the department, they were less than pleased. In fact, they were plenty steamed.

So they complained, and this week Cohen is back in his State of Illinois office -- somewhat mystified and more than a little upset. He says he's a friend of Bell's, has been since Bell held the job of commissioner of education in the Nixon administration and he was just trying to be "of whatever help I could be" to the secretary-designate as he prepared for his confirmation hearing.

"Who knows more about that department than one of the chief architects?" he said.

At Bell's confirmation hearing, Sen. Jeremiah Denton (R-Ala.) asked the secretary-designate to respond in writing to a question on Cohen's status at the Education Department. The answer came back: Cohen is not now and will not be in the future a paid employe or a volunteer worker for the Department of Education.

A spokesman says Bell has no comment on the incident, but Cohen says the subject of his working for the department never came up in their discussions.

Meanwhile, he's concerned about what impact the brouhaha will have on his ability to lobby for education in Illinois. "It sure makes my job a little more difficult," he sighed.