Germany is being bombed, and so is London. The US is fighting the Germans, the Italians and the Japanes. But during these total wars, were there any civilians flying to and from these countries? Say I'm a German businessman during the early 1940s. Would it be considered strange for me to walk the streets of London? Say I'm a German businessman, would sitting down at a law office in New York, signing a contract with an American company, be unthinkable? And in that case, at what point of a war would it become unthinkable?
I do know, at least, that third country nationals were able to use neutral nations as transit hubs. Many of the American officials who went to London in the early days tended to travel by clipper to Spain to avoid war risk, and from there to Britain. Americans could have just as easily transferred on through Vichy France into Germany if they had the proper visa approval prior to December 10, 1941.
Obviously, short of being an ambassador on an official mission to reestablish diplomatic relations with a nation you are at war with, you're not likely going to get a visa to allow access to an enemy nation. But, I don't believe I've ever read of visa restrictions on third-country nationals. Maybe someone else has actually heard of some. I'm pretty sure Argentinians could not have been granted visas to the United States given the embargo of fuel rations that went on due to Argentina's pro-axis leaning - however, if they could secure a flight to Spain they would have probably been welcome in Germany.
And. If you believe the records of the US Joint Chiefs of Staff organization devoted to petroleum, there were significant fears that Avgas was being diverted from the Caribbean to a German airline that was offering service in neutral South American and African nations. The Americans got around that problem by issuing strict bunker control measures at the refineries (accurate information keeping as to which ships take on fuel and how much), and, by investing resources into Pan American Airlines to force the Germans out of the marketplace competitively (from an unrelated narrative).