I am, however, going to answer the challenge directly. Before I do, though, I'll explain why the question would still be a monumental red herring even if it could not be answered. It wouldn't actually matter if there was no country in the world that allowed foreign nationals to vote on constitutional matters, because excluding foreign nationals is not actually what is being proposed here, or at the very least it's not the main thrust of the proposal. The suggestion is that some English people who hold both residency and citizenship in Scotland, in other words people who are not foreign nationals, should be stripped of their right to vote. You only have to think of it in those terms to realise what a total non-starter this proposal is - even if it was remotely desirable, which it is not.
But my answer to the challenge is very simple, and it's the United Kingdom, which allowed non-British Commonwealth citizens to vote in the referendums on European membership if they were resident in the UK. That includes, for example, citizens of India, a country that contains eighteen per cent of the entire population of the world. As I was only asked to provide one country that allows foreign nationals to vote in constitutional referendums, I don't need to go any further than that, but there will almost certainly be other examples if anyone wants to trawl through the electoral rules of other countries. One possibility is New Zealand, which allows all resident non-citizens to vote. If there's any exception to that general rule for constitutional referendums, I haven't been able to find any sign of it yet.