Not only do capitalists promote right wing populism (because as you say, it doesn't challenge capital), they similarly squash left wing populism.

Look how many progressives were primaried out recently in the US because of their anti-genocide stance and other leftist values.

Far right nationalism doesn't benefit capitalism the way you think it does. Do you have any evidence to go off of that big corpos are actually pushing far right agenda. In germany in Saxony for example the medium sized companies are running ad campaigns against far right extremism since we rely on immigration and skilled labor from abroad since we don't have enough people to fill all the jobs ourselves. No immigration would literally hurt the economy. I don't know what you're on about.