PRAGUE—An estimated 50,000 protesters rallied in Prague’s iconic Wenceslas Square in mid-May—the center of 1989’s Velvet Revolution and the earlier anti-communist revolt in 1968—amid rising fears that the Czech Republic could follow neighboring Hungary and Poland in sliding toward authoritarian rule. The mass protest marked a fourth week of growing demonstrations, kicked off by the surprise announcement on April 18 that an ally of billionaire Prime Minister Andrej Babis would take over as the justice minister, just a day after Czech police had recommended that Babis be prosecuted for fraud.

The protesters worry that the previous justice minister, Jan Knezinek, was pushed out as the high-profile investigation into corruption allegations against Babis had wrapped up. ...