tl;dr

Change wasn't total. Protestant princes viewed the Emperor as legitimate, and usually wanted protections and freedoms. They used a lot of pre-existing strategies, like the creation of alliances and legal challenges, but decreased their uses of violence. Much the same can be said of the Emperor, but from the opposite end.

I. The Importance of Westphalia

It's safe to say that the importance of the Peace of Westphalia has historically been overstated. The major change that came out of it was the cessation of Landeshoheit (literally, territorial supremacy) to the constituent princes of the Empire, but some historians have argued that this was essentially a de jure admission of what was already de facto the case.^(1) Wherever you fall on this debate, it's very much evident that the princes of the Empire had a lot of practical control over their own affairs before the Thirty Years' War. Though of course revolts and internal or external alliances were by no means unheard of outside of the Empire, the sheer frequency with which Imperial princes attacked the Emperor or the Empire's constitution, created internal leagues, and concluded treaties with outside powers was quite unusual.^(2) This issue became especially severe from the reign of Rudolf II (1576-1612).

Relations between the Emperor and Protestant princes tended to be somewhat strained. Protestants had used all of the autonomy-grabbing strategies they could, pretty much: they formed leagues (famously the Schmalkaldic League, 1531-1547), conducted outright wars against the Emperor (1546-1547, 1552) and within the Empire, made external treaties, and exploited constitutional mechanisms to halt attacks on their rights. This latter mechanism was very common. Legal complaints were launched about perceived threats to anti-Protestant reaction all the time, and from 1555 the constitution granted a variety of protections to the Protestants. It allowed them the principle of cuius regio, eius religio (whose rule, their religion) and legally guaranteed the confessional statuses of various minor polities, such as Imperial Cities.^(3)

With the end of the bloody Thirty Years' War - again, an outright war against the Emperor on at least nominally religious grounds - there were constitutional changes. The rights of the Protestants were made formally indefinite and extended such that neither side could ever dominate the other. One such provision was the itio in partes (division into parts) in the Reichstag, by which the institution would be divided into its respective confessional parts on any point of major disagreement. Judges on the Reichskammergericht (Imperial Chamber Court) were to be evenly Catholic and Protestant. However, the fear of religious war remained, and didn't really dissipate until the early 18th century, so I'll treat here up to the end of the reign of Charles VI (1711-1740).^(4)

The question remains as to whether Westphalia changed how princes saw the Emperor, and the answer is a bit of an indecisive "sometimes". Certainly, some princes showed an increased interest in acquiring power outside of the Empire and becoming European-scale powers in their own rights; famously, Brandenburg, Saxony, and Hanover all got non-Imperial crowns over time. Enmity towards Emperors and their frequent attempts to centralize power around themselves continued, but even in extreme cases of friction there was never an attempt to declare the institution of the Empire as illegitimate in itself. Brandenburg-Prussia is the paradigmatic example of a princely polity which tried to assert itself in the post-Westphalia Empire, and even it never explicitly challenged the Empire in general, or even its institutions. Friedrich Wilhelm I (1713-1740) generally just protested that the expansionism he was doing was legal, not that the law was illegitimate or irrelevant; sometimes he was even stopped through legal proceedings against him.^(5) The legitimacy conferred by being in the Empire was a powerful incentive in its own right.^(6)

II. Strategies and Aims

One of the important outcomes of Westphalia was that there were now lots more foreign guarantors of peace in the Empire. The major players were France and Sweden, both of whom had formal rights of intervention if things got too heated - though it's probably notable that the French served as an excellent common enemy for most princes due to their expansionist policy! This meant that starting wars over religious matters was a very risky business, and thus not something most princes were willing to do. The favoured way to go was to exploit the legal structures of the Empire and its notorious lethargy to make things into faits accomplis - court cases could literally take over a century, after all.

Protestants also became incredibly capable in the use of what was essentially political procrastination, ensuring there could be minimal progress on anything that threatened them. Barbara Stollberg-Rilinger has argued that from 1653, when the Reichstag was made permanent, conflicts were symbolically encoded and perpetualized in order to try and reduce the extent to which those conflicts spilled out into the "real" world.^(7) Similarly, they were enthusiastic litigators. These ways of dealing with conflicts did one of two things. They either essentially deferred confrontation indefinitely, giving the situation time to become normal and less controversial, or they used the fact that the Empire's stability now rested on justice and confessional equality to make it too dangerous not to concede. Fundamentally, these strategies were pro-Imperial - they relied on a strong Emperor to enforce Imperial mechanisms, and a strong Empire to guarantee legitimate execution.

Another "traditional" strategy the Protestants used was the construction of leagues. These could not be explicitly directed against the Emperor, but other than that they now had considerable legal freedom in this regard. These weren't even necessarily confessional, and could just be broadly for princely freedoms. The Rhenish League, founded in 1657, is a good example of this, spanning different confessions and having support from multiple pro-princely-autonomy forces (most importantly France and Philipp von Schönborn).^(8) However, Protestant princes generally showed a particular interest in these projects because of their religious worries.

The Emperors were, by and large, not passive in this process. Rather, they actively tried to reassert their authority over all areas of the Empire, including in religious matters. Just like other princes, they mostly used peaceful strategies, but in rather different configurations. As the formal enforcers or at least heads of most Imperial institutions, they could try and selectively enforce laws and other norms.^(9) In fact, enforcement in general could confer them with legitimacy in the eyes of those princes who were in favour of a stronger Empire - this seems to have been the aim of Charles VI in the East Frisia and Mecklenburg cases in the 1710s and 1720s.^(10) They also made international and internal allies to give their claims extra leverage. In international wars, they occasionally tried to reclaim territories on questionable legal bases - for instance, in 1703, Leopold I (1657-1705) tried to reclaim part of Alsace using a contentious part of Westphalia.^(11)

III. Conclusion

Fundamentally, aims and strategies were largely stable from the pre-1618 period for most princes, the Emperor included. The main difference is that the opportunity costs for any kind of confessional violence rose sharply, and the robustness of legal or stalling methods rose due to the constitutional changes made by Westphalia. Protestant princes' aims were roughly the same, maintaining their privileges and protections - and preferably expanding their autonomy. To do this, they needed strong and lively institutions and/or good allies to guarantee what they were doing. The Emperors wanted hegemony in the Empire. Westphalia was important, but it couldn't revolutionize the interests of Imperial actors.