LotR (& the Legendarium as a whole) does present 'traditional' Western (ie 'Christian') values without irony or condemnation. I think this is enough for most critics to condemn it. It is the epitome of 'dead white male' culture (& from our perspective most of the characters
are dead white males, being that the events of the story took place 7 or 8 thousand years ago.
Aragorn tells Eomer that moral & ethical values do not change, & are the same among Elves & Dwarves as they are among Men. This is a clear rejection of moral & cultural relativism, that all moral codes are equally valid. In short, Tolkien is stating that
some values are better than, suerior to others, - even
worse, that some are Right & some are Wrong.
It seems to me that
this is at the heart of the reason some critics so dislike Tolkien's works - they may
like irony, but are not offended by its absence to that degree.
Of course, this eternal moral value system does pre-suppose some ultimate source exterior to Mankind. If accepted, Tolkien's position requires people to aknowledge an objective moral code, (& an objectively existing 'source' of that code). Hence, LotR belongs with 'pre-Enlightenment' works - as Tolkien said it is a 'heroic romance'. I think this is why many of the very same critics who condemn LotR have taken HDM to their hearts.
What I find most interesting though, is that these critics are not able to accept Tolkien's philosophical position even
within the secondary world. They are incapable of not projecting it onto the primary world. Shippey has said that many of Tolkien's early critics read the book, responded to it, but then realised they didn't like the fact that they had responded to it & so turned on Tolkien (paraphrasing his words in the documentary 'JRRT: A Film Portrait'). The work touches a chord in them that not only do they not
want touched, they hadn't even believed that chord was there to
be touched. Its like an extreme form of
reaction-formation
Or something like that....