What's your source for this assertion?
I see it as the opposite. Persecution absolutely happened under Protestants (including the first Anabaptist martyrdom), but as far as I can tell, the most severe persecution was under Catholics, for whom the use of the sword to exterminate "heretics" was a tenet of church teaching taught by papal bulls and church councils.
This book by an Anabaptist convert says that Catholics were responsible for 84% of executions of Anabaptists:
http://www.wittenberg2017.us/uploads/3/ ... nglish.pdf
Schaff says (https://ccel.org/ccel/schaff/hcc8/hcc8.iv.iii.xvii.html),
And when I look up the worst of the persecutions (detailed in the link below for example), they were mostly done by Catholics. Again, there certainly was persecution from Protestants; but where there was a measure of toleration, such as under Philip of Hesse, or in Strasbourg where Martin Bucer was the Protestant leader, or in the Palatinate after the 1530s when the Protestant electors took over the government, or in the Netherlands under the Protestant William of Orange, it was mostly under Protestant leaders.In Germany and in Austria the Anabaptists fared still worse. The Diet of Speier, in April, 1529, decreed that "every Anabaptist and rebaptized person of either sex be put to death by sword, or fire, or otherwise." The decree was severely carried out, except in Strassburg and the domain of Philip of Hesse, where the heretics were treated more leniently. The most blood was shed in Roman Catholic countries. In Görz the house in which the Anabaptists were assembled for worship was set on fire. "In Tyrol and Görz," says Cornelius,145 "the number of executions in the year 1531 reached already one thousand; in Ensisheim, six hundred. At Linz seventy-three were killed in six weeks. Duke William of Bavaria, surpassing all others, issued the fearful decree to behead those who recanted, to burn those who refused to recant.... Throughout the greater part of Upper Germany the persecution raged like a wild chase.... The blood of these poor people flowed like water so that they cried to the Lord for help.... But hundreds of them of all ages and both sexes suffered the pangs of torture without a murmur, despised to buy their lives by recantation, and went to the place of execution joyfully and singing psalms."
https://www.gracegems.org/C/persecution ... ptists.htm
(This is from the book "Mennonites in Europe" by John Horsch)