To be honest, I think foreigners don't think any differently of BA, whether they fly a British flag, or a Spanish one (pure example). In the end, people abroad will know BA as being either a good airline, or a bad one, regardless of the cartoons on the tails.
However, BA has to answer to it's investors demands (within reasonable limits), after all, it's their (the investor's) money; they should have a say on most aspects of running the airline, including the way the planes look.
Whilst I readily accept many foreigners, enthusiasts loved the schemes, I have met many of my father's collegues (American, British, South African, Australian businessmen), who preferred
* the old "To Fly-To Serve" scheme.
In the end though, they didn't really care, so long as the service remained the same, and the seats continued to get larger
*In italics, because although they preferred, they didn't really care what the plane looked like, as long as they could see the words "British Airways", somewhere!