The Senate early yesterday passed and sent to President Reagan a bill to exempt a Capitol souvenir shop from District of Columbia sales taxes, ending the latest round in a small but symbolic dispute over home rule.

Run by the nonprofit U.S. Capitol Historical Society, the tiny souvenir shop became the focal point of a fierce feud over local tax exemptions between Congress and the city government, which claimed the society owed it $740,000 in back taxes for the noneducational items it sells.

The city argued that the society should not be exempted from D.C. sales tax just because it operates from the Capitol, when it sells general items such as cameras and film, which the city says compete with local merchants.

"We believe the bill sets a dangerous precedent," said Johnny Barnes, staff counsel to Del. Walter E. Fauntroy (D-D.C.).

It clears the way for organizations that provide services on Capitol Hill or that sell office equipment there to claim exemptions from the sales tax, he said.

Walter Lund, associate director of the D.C. Finance and Revenue Department, indicated that the bill could also indirectly affect other groups selling general items on federal property, such as at the White House and Supreme Court.

"It was something we felt we had to test to collect sales taxes," Lund said. "This bill says to the city pretty much 'Hands off.' "

Congressional sponsors of the exemption bill charged that the city was attacking the very foundation of Congress' sovereignty and its constitutionally protected jurisdiction over its own home, the Capitol Building.

"The power to tax implies many other powers--the power to audit, to inspect, to enter, to confiscate for nonpayment and to require reports," said Rep. Robert McClory (R-Ill.). "The Home Rule Act . . . was never intended to extend to such far-reaching jurisdiction . . . ."

If signed by President Reagan, the bill would put to an end a court suit the District brought against the souvenir shop in 1979, claiming the sales tax for commercial sales since 1966.

The U.S. Justice Department countersued on behalf of the society and won in U.S. District Court in September, but the District filed a notice of appeal.

The society, among other things, restores paintings in the Capitol and produces historical calendars that members of Congress hand out to constituents.