The title of the post sounded like non-AA passengers can access FlyerTalk but not AA passengers. Wow, they have recognition software which can identify AA passengers and non-AA passengers?!
It is common for computers in public places to have chat sites or public forum sites blocked. I agree that it has nothing to do with BA, it is simply the company maintaining or providing Internet access to computers at BA lounge at MXP is doing. It is not that the service provider went through content of FlyerTalk and decided offensive. At public forum sites so many different subjects are covered, some serious political topics, some environmental issues, some religious issues, and some sexually explicit topics. It is common practice, even in the U.S., to block public forum sites such as FlyerTalk on public computers.