Not only may one not wish a person merry kratzmach, as it is mechazel yidei ovrei aveirah, there are clear mishnayos, gemara and shu”a about doing things that make goyim happy before their holidays, so they shouldn’t thank their god. I don’t remember off hand to what degree these apply to christian holidays, but extending a greeting which acknowledges a holiday which is at the very least avodah zara for us – to the point of being yehereg velo yaavor – is very simple.
Were it not for the fact that an anonymous post online is not aidus, I’d very much like to know the identity of the “rav” who did this; it’s disqualifying just as any other aveirah. And the worst part is how it leads other jews to follow his example.
Regardless of how goyim today view the new year, it was founded on the basis of religion. Just as we cannot acknowledge Halloween, we are prohibited from acknowledging new years.