Maybe? It could be that Vale knights would particularly insist on the link between the Seven and knighthood, given their cultural traditionalism on everything else, as opposed to Robert who clearly didn’t give a damn when it came to knighting worshippers of the Old Gods.
It wouldn’t have been appropriate to give the second born son of the Lord of Winterfell (formerly a kingdom) a foreign knighthood as it was lower status than Ned’s pre-existing titles. If anon’s talking about Ned actually joining the Knights of the Vale; he couldn’t possibly. He’d have to swear allegiance to House Arryn in a way that would make his duties to Winterfell and House Stark impossible. His allegiance lies with Winterfell, it wouldn’t make sense for him to be offered and accept a position in a foreign military force. If this had happened in the 15th/16th century for instance several eyebrows would be raised and it’d definitely be seen as an insult.
I don’t think that’s how it works. No one thought it was inappropriate for Jorah Mormont to be knighted, even though he was Lord of Bear Island. And as a second son, Ned didn’t have a title.