German nobility counted all of one's ancestors. Sure, father's line was most important, but they preferred marriages to those whose full pedigree was noble/dynastic.
For example (and this is going forward aways in time) Sophia of Hanover didn't want her son to marry (the not yet Queen) Anne, because she didn't like the Anne Hyde connection. She was eventually able to make her peace with the d'Olbreuse connection made by her son's actual spouse, because A) it got him a greater inheritance and B) she couldn't really dissuade him from the marriage anyway. Neither marriage would have been morganatic, but both were seen as being in pretty poor taste.
So it's less that the marriage between Max and Liz would be seen as morganatic, but more that it would have an unappealing connection that might have smelled a little bit too much like a morganatic connection for a superstitious man like Frederick III to care for it. If England brought any tangible diplomatic benefits I don't think anyone would have cared, but I think Frederick would have probably turned up his nose at the suggestion, regardless if Liz was a king's daughter or not (would she really have been called a princess? I understand king's daughters were called 'ladies' in England at the time).