Germany wasn't a unified country until 1871 and can't really be described as Lutheran. Germany had Catholics, Lutherans, Calvinists and others. There was a solid Protestant majority in the north and a solid Catholic majority in Bavaria, the largest state, which is in the south. Also Austria was solidly Catholic. After German unification, Bismarck and the Prussians were running the show and engaged in the Kulturkampf (culture struggle) against the Catholic church. Not over whether Catholicism should exist but more over political control, not least over schools and such. But it's another story.

So Hitler was from Austria (and spent a lot of time in Bavaria too) and as one would expect then he did come from a Catholic family background. Many book shave been written on his relationship to religion and christianity. (e.g. Rissmann, Hitlers Gott) What's certainly quite clear is that Hitler was not a practicing christian nor a fan of the Catholic church. However, he also told party officials not to leave the church and generally did not want to alienate people by getting into too big of a fight with the church. Hitler voiced his dislike of the Catholic church privately but not in his big public speeches. The party officially tolerated catholicism and other christian denominations. A big exception to that would be the Jehovah's Witnesses (then known in Germany as 'Bible students') who were sent to concentration camps. But especially considering the Nazi Party's Bavarian origins, they'd have had a hard time getting started if they'd had an explicitly anti-Catholic agenda. Then there were guys like Himmler who had his own weird Germanic neo-paganism and really hated all forms of Christianity. But Hitler was not a fan of that stuff either.

So Catholics were not punished simply for being Catholic. However there were Catholic and Catholic-allied schools, political parties, trade unions, newspapers and so on, which were shuttered and people imprisoned, punished or even executed. But Catholicism per se was not the problem; any priest who spoke out against the regime, any school that didn't teach what they wanted taught, would be in trouble no matter what their religious label was. There were priests of all stripes on both the sides of opposing and collaborating with the Nazis. However, since there had been more state control over the Lutheran and Calvinist churches since Bismarck's day, there was less resistance to nazification (swearing loyalty to the regime, banning "non-Aryans" and such demands) there relative the Catholic church.