That is 100% not true. The Bill of Rights absolutely applies to non-citizens.
But I have full understanding for people who are in a situation that the US is still the smaller evil.
Do most EU nations have constitutional protections as strong as the US bill or rights?
The constitution is only as strong as the institutions that defend it. The U.S. is not there yet but the political nature of the courts and the judiciary are an anathema to a Brit.