Demographics and literacy rates: the great amoebas of medieval and early modern scholarship. As Tom Scott, one of the leading socio-economic historians of Reformation Germany, put it: "For the moment, all that can be said is there is no agreement among historians on population figures for Germany in [1500-1600], or on their means of calculation."
So allowing for some ridiculously broad ranges:
Euan Cameron (Reformation/cultural historian) estimates that vernacular literacy rates in cities ~1500 ranged from 30%-50%. This would have been deeply stratified by class. It's actually an open question whether there would have been a gender gap in 1500; later literacy rates would favor men until into the modern era. Contemporary satirical literature sometimes assumes that women are more likely to read than men, that this is not the right order of things and so men must learn to read. But that could just be an exaggeration, another "women are taking over!!!11!1!" joke - boys rather than girls had formal opportunities for education before the Reformation. (Afterwards, there is more evidence that [Catholic] convents ran schools for local girls.)
Assorted studies of the 1500-1600 urban population have given rates of urban:total population anywhere from 8.5% to 16% in 1500-declining to 13% by 1600.
There would also have been rural clergy who were more likely to be literate after the Reformation than before, or at least before 1450. Fifteenth-century ecclesiastical records are filled with rural parishes asking the diocese for a new priest because theirs does not know religion/cannot preach - meanwhile theologians and printers are working overtime to produce handbooks for priests, which ought to have supplied that knowledge to those who could access it.
So overall, I think, you'd say maybe 10-15% of the German population was literate to the point of being able to muddle through a vernacular Bible in the early Reformation years.
Did the Reformation/Protestantism change things? Sort of but not really - mass literacy in the West is, quite frankly, a modern phenomenon. (For example: white-universal literacy in New England is only achieved by 1815, later in the South; racist education and social circumstances kept rates far lower for black Americans). There is some evidence that "learning to read for the Bible" played a factor: Lutheran Scandinavian countries were the first to reach universal literacy, with that as a goal. Some studies of the education of enslaved people in the U.S. have suggested that by the 19th century, some slaves were in fact allowed/encouraged to read for the purposes of religious instruction, that actually learning to write was the forbidden skill of white fears.
Definitely the 16th century continued the trend of better educated clergy. Pastoral care handbooks and especially collections of sermons/sermon skeletons were enormously popular in 16C print, and they were definitely used by preachers to preach. (Sermon authors complain that pastors are taking their words straight-up instead of as a guide to be expanded upon.) But this was not an exclusively Protestant phenomenon. Education for Catholic clergy was also systematized, gradually, over the 16th and 17th centuries.