If the "people" do not "accept" the result of the previous vote, but are more accepting of the results of the new vote, there's nothing wrong with it. That's kind of how democracy works. It may feel wrong, but if the people's opinion change, then so can the result
I think it is more important that the second vote could be more definitive. Hopefully it would split more than 2% one way or the other this time. And indeed, if it once again goes leave, then I think it's reasonable for the UK to leave basically right away, no plan or anything. It's only right