I don't think this is true. A brief search finds nothing that says he was, and several places that don't say he was where I'd expect them to. E.g. http://www.weatherimagery.com/blog/president-woodrow-wilson-... https://en.wikipedia.org/wiki/Woodrow_Wilson#Civil_rights
The Wikipedia page ignores all the other articles (do the search) about Wilson's beliefs, friends, and civil rights record. It is also ignored in HS history books just as President Lincoln's dealing with the Dakota is ignored. Let's also remember he was happy about the biggest KKK march on DC in US history. Never mind his dumb meeting after WWII in Paris.
"Not being a member of the KKK" doesn't mean someone wasn't a racist. If he was a racist, we can say that without saying he was a member of the KKK. You'll note that I linked an article titled "President Woodrow Wilson was a Racist", which successfully accomplished this.
:) "perl harbor", very HN typo ...
I think there were enough folks that would have cared just from a self preservation view if the UK had gotten invaded.