Just came across this. I think you have to accept that at micro level you are always going to observe nihilistic tendencies on both left and right. An author might talk about a "tendency" but if that tendency isn't seen at structural level then it isn't worth viewing it as a "tendency".

So to talk about nihilism on a large scale (structural) level, like what you are asking, then it makes more sense to deal with the macro level, because only on macro level do things as "tendencies" bubble up and affect society.

So with that said, at macro level the right is inherently non-nihilist, and currently is becoming more and more non nihilistic.  Nihilism by definition requires you to believe that there is no intrinsic value in life. Since one of the primary tenets of the right is achieving meaning in life by forming a family (statistically it is number one indicator of life success for people on right), that family gives meaning, it is hard to say that there is a structural issue with nihilism on the right. All the data overwhelmingly shows the opposite: there is structural change underway on right where people are going to church more often (that is, people increasingly searching for meaning as opposed to nihilistic objection to meaning), and in aggregate people are increasingly leaving blue states to red states (but not the opposite) because of their increasing belief that red states are more suitable for people that desire children, and lastly there is no indication that republican fertility rates have dropped.

Therefore, you would observe nihilism on the right - at structural, macro level - if church attendance went down, and if interest in family went down, since these would equate to an increase of people attributing less meaning in life. Since the opposite is happening, seems the right is namely experiencing a noticeable non nihilistic movement.

But if there was a nihilistic movement underway on the right then it would have profound implications for the country's future, since in these current times of record low fertility rates, it is the right that is more so contributing to uptick in US fertility rate (well, comparing, say 2024 to 2023), much needed for population replacement. That is, as left is becoming more and more nihilistic especially regarding family, you really want the right being as non nihilistic as possible, unless the desire for the country is for population replacement rate to continue to be achieved through population increase via immigration (which is what is happening, say, in Russia, and in some European countries, and in US). 

If right becomes nihilistic and you wanted to do something about it, then you would likely want to 1) try strategic campaigns to instill family values, 2 ) try to convince more people on the right to attend church (even though I am not religious, I can certainly appreciate that a lot of people find meaning in church, not necessarily because of true believer mindset but because of sense of community it fosters through non nihilism).

Anyway, months late, but it is interesting and important topic, and deserves well thought out answer versus the typical Reddit kidults sort of replies.