Yes, there were. Ideological and military conflict between Catholics and Protestants is a defining feature of German history in the century (and more) following the start of the Reformation. It's a pretty wide subject, so I'll summarize a lot. Please ask if you want me to elaborate on something.

The very first reaction to Luther's ideas was already hostile. The authority of the Holy Roman Emperor was closely tied to that of the Pope, especially as Emperor Charles V was trying to build a reputation as the protector and leader of an united Christendom, so opposing the Catholic Church had wide secular implications as well. Several of the Empire's most important states, including three of seven electors, were prince-bishoprics, and the Church had a lot of property and influence in the realm. In 1521, the Empire convened in the Diet of Worms (city, not animal) where Luther was declared a heretic and excommunicated, forcing him into hiding.

However, even without his direct involvement, scholars and laymen alike were influenced by his writings, and several very different branches of Protestantism started to spread. The Empire's fragmented nature made it possible to individually convert small city-states, either through persuasion or by force, which became little pockets and spiritual centers of their respective sects.

Even in conflicts where Protestantism wasn't the main motivator, people were eager to use religious rhetoric to justify themselves and rally their followers. One early example was the Peasants' War (1524-1525), where about 300,000 peasants took up arms, making it Europe's largest popular rebellion before the French Revolution. Ideological matters aside, people on all levels of society had material interest in resisting the church and trying to seize some of its vast wealth.

Religious strife continued. The next major conflict was caused by the formation of the Schmalkaldic League, the Lutheran princes allying against the Emperor. The Schmalkaldic War started in 1546, and in 1555 the Peace of Augsburg promised the princes religious freedom: they were all free to choose the religion of their own realm. However, even on paper (nevermind in practice), this still left a major issue: people who didn't share their prince's faith.

That eventually became especially relevant in Bohemia, where the Catholic Habsburgs ruling it tried to impose their religion upon the Protestant populace. This was the cause of a rebellion in 1618, which soon erupted into the Thirty Years' War, one of the longest and bloodiest wars in European history. It involved most of Europe and it has been estimated that at least 1/3 of Germany's population perished in the decades-long fighting and looting. Yes, political issues soon became the main motivator, and the war expanded beyond religious lines, but originally it was definitely a conflict between Catholics and Protestants, and religious rhetoric played a part the whole time. The Peace of Westphalia (1648) strengthened the Peace of Augsburg, adding religious freedom for individual subjects as well. Things finally calmed down a bit and the borders between faiths started to stabilize, though a lack of major wars obviously didn't mean a lack of animosity, and the Empire's authority as a whole had taken a major blow, contributing to its slow decline.

These are just the three largest military conflicts caused by the Reformation in Germany. In between, there was no end of theological and political strife, and conflicts in neighboring areas tended to spill over into the Empire as well.

Today, Christianity in Germany is almost evenly split between Catholics and Protestants, and as far as I know they get along relatively well; but this hasn't always been the case. The major difference to the Isles is probably that the schism hasn't really been a big issue in the last few centuries, and doesn't have the same connection to nationalism, so it doesn't come up quite as often.

Sorry if I misunderstood and you were asking more specifically about recent history.