I wrote years ago What Tolkien Disliked About Narnia, and my mind had not changed about this until recently. Holly Ordway, the author I mentioned yesterday in Notes From an Unliterary Reader relates that this is greatly overstated, tracing much though not all of it back to Humphrey Carpenter. Her method is very strict with regards to original sources, rather than two generations of critics quoting each other about who said what to whom. She finds few direct references of what Tolkien thought about Narnia, but looking at the few unarguable ones, she finds his disapproval mild and his approval considerable. For example, he had a bookshelf for the grandchildren when they came over, and this was watchfully curated, with few volumes in total, as he was a bear about encouraging good taste in literature. All seven Narnian Chronicles were on the shelves, elsewhere estimated at about thirty volumes in total. Beatrix Potter and Lewis Carroll were also believed to be on the shelf, but I have not found any further books identified specifically. He remarked in correspondence that he was glad that his recipient had discovered Narnia, and that the books had become "deservedly popular."
The negatives are that he commented "I hear you've been reading Jack's [Lewis's] children's story. It really won't do, you know! I mean to say: 'Nymphs and their Ways, The Love-Life of a Faun'. Doesn't he know what he's talking about?" (italics mine) and "It is sad that 'Narnia' and all that part of C.S.L.'s work should remain outside the range of my sympathy, as much of my work was outside his." But the former was after listening to the first few chapters read aloud, and given the italicised part is easily attributable to the standard mythology of fauns/satyrs as rapists, and Lewis changed what books appeared on Mr Tumnus's shelves thereafter. As to the latter, Tolkien did express distress at Jack's mixing of myths and "too obvious" allegory, as his works are less so. Still "Leaf by Niggle" is allegorical, and the opening section of Silmarillion is clearly allegorical to my eyes, so I am not sure he is being quite fair. Though I take his point. Aslan executed on the
Ten Commandments Stone Table and then resurrecting shortly thereafter is too blatant for my taste as well, however many modern readers are oblivious to it. "Outside the range on my sympathy" should be regarded as no more and no less than what it says.