Was it really just about religion, or was it really about the power of the Emperor and the rights of the princes? Most accounts I have seen have tended to portray the 30 years war as being about the attempts of the Habsburgs to centralise the HRE and the rights and powers of the Emperor over the princes.
I don't think that's completely correct. In its first phase, the 30 Years War was about religion on the one hand and the Habsburg rule over Bohemia on the other hand. In this phase, Frederick of the Palatinate was only supported by very few princes; even most of the protestant princes didn't support him (because seizing the crown of Bohemia was considered to be a completely illegal action even by the protestant princes).
Then, things got more complicated: After the Habsburg troops had occupied the Palatinate around 1622/23 and the Spanish-Dutch War had started again, France feared the new strong Habsburg position on the Rhine, Denmark feared that a Habsburg victory in the Netherlands would endanger their somewhat hegemonial position in Northwestern Germany and England feared that a Habsburg victory in the Netherlands would lead to a new Spanish attempt to invade England (plus Frederick was married to a daugther of the English king). Denmark, the Netherlands and England, however, were also motivated by religious motives, since they were all protestant and wanted to protect their protestant brethren in the HRE.
This is why the three powers formed a league against Habsburg, supported by France and together with the few protestant princes who had supported Frederick V. during his Bohemian adventure.
For Ferdinand II. of Habsburg, who was Emperor at the time, centralisation of the HRE was never a priority: Ferdinand was a catholic fanatic. All he wanted was to roll back the reformation in the HRE. So, from his perspective, the war was all about religion, until his death in 1637 (his military commander, Wallenstein, was rather bewildered by that and tried to push him into the direction of political centralisation rather than religious roll-back, but Wallenstein ultimately failed). But of course, in order to do so, Ferdinand had to strengthen the power of the Emperor in the HRE and that alarmed powers like Denmark, the Netherlands, France and England.
After the Habsburg had also beaten Denmark in the Danish-Lower Saxon War of 1625-1629, Sweden intervened, partly to protect protestantism in Northern Germany from Ferdinand's plans to roll back the refromation, partly because they feared a strong Habsburg position in Northeastern Germany. So, was this a religious or a political motivation to intervene? I would say: both at the same time.
In short: there is no clear cut distinction in the motivations of the acting persons between "political" and "religious". For some (France), the political reasoning prevailed, for others (Ferdinand II.), the religious reasoning prevailed and for most, it was a mix of both kinds of motivations (like for Denmark, Sweden, Netherlands, England). Without the political motives, the 30 Years War would have been a completely different war with different coalitions, but without the religious motives as well.
The problem about the way Paradox depicts the League Wars is that they decided to completely cut out the religious dimension in favour of the political dimension, which is completely ahistorical. Yet, it would also have been ahistorical to cut out the political dimension in favour of the religious dimension. A game probably just can't model something that complicated.
