The UK has always shown the greatest respect to all countries around the world. So no, the UK not recognising the EU as a country and treating them with the same privileges as one shouldn't cause any problems, it isn't one. I would go further, and as our recent success with the French quarantine bilateral agreement last weekend shows, the UK should just refuse to recognise the EU as a legitimate organisation at all. We have a list of proscribed organisations it could fit quite easily in however...
As for reneging on previous agreements sovereign nations make and break agreements all the time. It is quite normal and sort of the definition of sovereignty, the reason the people, by massive majority, voted for brexit again and again in the first place.