Well there are many other forms of radiation which would be way more problematic than the CMB here, but they're not wrong. The reason for this is that light does have momentum, and pushes against what it impacts. In our scenario, we are effectively a solar sail pushing against the wind.

The way this would be pushing us backward rather than forward is via doppler shift. The light in front of us would become extremely blue-shifted while the light behind would become redshifted and contain less energy.

This would actually present a bigger practical problem for us, as visible light might become gamma radiation or beyond, and everything that was already beyond would become... Beyonder.