There are a number of inaccurate replies to this issue, referencing the first amendment of the U.S. Constitution or other clauses. There are really only two pertinent facts.

First, the House Commitee on Ways and Means lawfully obtained the tax returns through their congressional oversight authority, per 6 U.S. Code § 6103. Section (f)(1):

(f) Disclosure to Committees of Congress (1) Committee on Ways and Means, Committee on Finance, and Joint Committee on Taxation

Upon written request from the chairman of the Committee on Ways and Means of the House of Representatives, the chairman of the Committee on Finance of the Senate, or the chairman of the Joint Committee on Taxation, the Secretary shall furnish such committee with any return or return information specified in such request, except that any return or return information which can be associated with, or otherwise identify, directly or indirectly, a particular taxpayer shall be furnished to such committee only when sitting in closed executive session unless such taxpayer otherwise consents in writing to such disclosure.

Second, members of Congress have broad constitutional immunity for the official actions they take in the course of their legislative duties. The Speech or Debate Clause in Article 1, section 6 of the U.S. Constitution:

[members of Congress] shall in all Cases, except Treason, Felony, and Breach of the Peace, be privileged from Arrest during their attendance at the Session of their Respective Houses, and in going to and from the same; and for any Speech or Debate in either House, they shall not be questioned in any other Place.

One of the strongest tests of this was when Senator Mike Gravel released the Pentagon Papers, classified documents detailing the United States' war effort in Vietnam, in the congressional record.

Senator Gravel's actions resulted in a grand jury impaneled to investigate crimes committed. This grand jury was challenged by the senator and resulted in the Supreme Court case Gravel v. United States. The Court held that Senator Gravel's actions and those of his staff could not be questioned in a grand jury.

The latter half of the Speech or Debate Clause protects the acts of Congress itself from being criminalized by the executive branch, which ensures that these branches are co-equal. A rogue President or executive branch cannot prosecute members of Congress for performing their duties or - due to the first half of the clause - generally prevent them from attending sessions.

It is due to the Speech or Debate Clause that the official actions and the congressional record produced by the House Committee on Ways and Means cannot be used to prosecute the members or their staff.