Yes the government fuels race tension by involving itself in something such as race that it can't truly "fix" as some would argue it could. Human racial tribalism isn't going away because forms are changed.
The hard fact for many is race is a structural part of our civilization. If you tore all the buildings down, the nations down, the armies away, the economies, race would still be going strong. Very strong. Like it or not, race is a massive part of human nature and won't be changed by government ever. Race might very well be the one true thing that cannot be controlled or manipulated by government whether governments like that or not (clearly many do not).
Example: In 500 years nobody will be talking about modern nations but race will still be a very big factor.