Lawmakers approved changes to the 2021 Child Protection Law, which banned the "portrayal or promotion of homosexuality or transgenderism" and had wide-ranging effects on education and the right of assembly.
Tisza, which commands the same two-thirds majority Fidesz once held, bundled the measure into a package of laws designed to unravel Fidesz-era legislation, following Orbán's defeat in April's election.
Minutes after the vote, Budapest said the European Union had agreed to release €4.2bn (£3.5bn) in funds frozen during the final years of the Fidesz government. The European Commission said last month that the Magyar government had addressed a number of "rule of law breaches affecting the EU budget" and urged EU leaders to unlock the funds and readmit Hungary to two key programmes, Erasmus+ and Horizon Europe.
Tamás Dombos of civil rights group the Háttér Society welcomed the adoption. "We are very happy that this got adopted. We've been fighting this so-called child protection law for five years," he told the BBC. "There have been problems with the bill submitted to parliament, but most of those problems have been fixed."
The Budapest Pride march this year went ahead without restrictions, a year after the Orbán government tried to ban it. Activists have called for changes to other Orbán-era laws beyond Tuesday's amendments.