No it doesn't. It asked whether paganism is a part of the Western tradition that should be conserved at a cultural level. Like any other goal of cultural conservatism, politics is a tool to achieve that outcome.
OP mentions three political movements and no others, leaving us to infer
it means to focus on the political. Certainly OP's last sentence requests
comment on paganism and "the Right", and certainly "the Right" is above
all a political term referring to political thought and political activity.
What follows below is an off-topic discussion on whether paganism has
any influence other than trivially chronological.
... I feel no compulsion whatsoever to agree to that very personal condition. Substitute out the theoretical justification and the social functions of the holiday are still broadly similar.
I do not know what you mean by "theoretical justification." Originally you
specified Catholic holidays and rituals. No religious holiday ritual may be
considered Catholic without its theological element, and that is an objective
rather than personal condition. I doubt it would matter if the dates were
changed, and in fact they varied in the early centuries of the Church, from
which we may gather the specific dates are of little to no import. There is
no doubt, however, that it would matter if the theology was changed.
In the case of any variation of New Years, an opportunity to assemble, renew the social connections that keep communities and families together, and collectively and individually examine the achievements of the year while using that understanding to develop goals for the next year.
You can say that New Years is an appropriate time for that because of Jesus's birth...
New Years is not associated with any religious event for the Catholics
or for any other denomination I know of.
...and (therefore) a period of significance for the human race that can be used for personal reflection, but from a practical and economic perspective it preserves an institution of a Pagan culture on terms that are largely agreeable to former Pagans because it puts their social and family organization to no inconvenience by changing their religion.
I don't see why proximity to Christmas should make it more convenient
to engage in personal reflection or to become a Christian.
The same thing applies to innumerable Latin American holidays where individuals of amazing virtue and spiritual prowess in Native American tradition suddenly became saints.
What same thing applies? My understanding is that all saints were exceptionally
virtuous Christians. They are all assigned "days" to be recognized by all Catholics,
and not just those Catholics living in the same neighborhood, although maybe
the locals are allowed to have an extra day off in honor of their localmost saint.
And I guarantee no pagan, Native American or otherwise, has ever been created
a saint, no matter how saintly he may have acted.
Note - also Halloween stuck around even when it had no real theoretical justification in a Christian context.
As of the 1907 version of the Catholic Encyclopedia "Halloween" directs to All Saints Day,
still an important date in the church calendar.
I'll give you Halloween as a pagan remnant, maybe, sort of. Halloween is I think a mostly
American tradition, though, and so is not a pervasive element of Western culture. Nor is
it really that important to American culture. Development of a costume party tradition is
sure to be possible without pagan influence, don't you think? I mean, some things are just
obvious fun, and transcend the need for specific religious or other cultural instigation.