This has nothing to do with BA it to be honest. It's just about your browser enabling websites to know your location and default to the local version of the website. You'd have that with other airlines just as you have had it with BA, and for all of the above, you can of course manually change the version of the website to UK, US or whatever you want. You can also change your browser settings so that they won't share location.

I've booked BA tickets on the UK version of the website, the French version of the website and many others, when in the UK, France, and literally dozens of other countries, and I can confirm that none of it is an issue be it at the time you fly or when it comes to BAEC/BAC credit etc.