A House Judiciary subcommittee voted unanimously to continue in operation but on a tighter rein the program of free legal services to the poor that President Reagan wants to end.

The Legal Services Corp., which helps the poor secure their legal rights, is viewed by some as a troublemaking organization fighting the establishment. But it also has considerable establishment support, including that of the American Bar Association and a number of conservative congressmen. One of them, Rep. M. Caldwell Butler (R-Va.), helped amend the bill in subcommittee in ways he hopes will persuade Reagan to sign it.

The bill, which the full Judiciary Committee is expected to approve next week, would cut next year's budget 25 percent below the Carter administration request to $260 million and would make a number of restrictive changes in the program's operation.

For instance, the board of directors of the corporation whom Reagan would appoint would have greater power to fire employes considered to be subverting the will of Congress and to withhold funds from local programs. Employes engaged in illegal lobbying would be subject to criminal penalties. States would establish advisory councils to serve as buffers between the agency and state and local governments. Class-action suits against governmental units would be forbidden unless in accord with policies laid down by the corporation's directors.

Subcommittee Chairman Robert Kastenmeier (D-Wis.) said the bill has been written so Reagan's advisers can tell him: "Mr. President, you will appoint the entire board and the board will run the program."