You knew it was coming. There have long been murmured comments, that Tolkien's swertings seemed not entirely sympathetic, and Lewis's Calormene's are rather obviously influenced by the Arabs of the British world, and their religion is regarded as a dangerous item (though its adherents are not irredeemable). Something similar happened when JK Rowling was uncomfortable with Lewis's sexism in the Chronicles of Narnia. In my discussion over a dozen years ago, I noted that in some ways Lewis's girls are more adventurous than hers. But that's (literally) another story.
These are the sort of battles that social justice warriors (sorry to use the hackneyed term, but I have no other here) tend to win over time, because of where they place themselves in the culture and who they can punish. Witness the recent withdrawal of the young adult novel by Amelie Zhao. However much Narnia and Middle-Earth are beloved now, they will go beneath the waves themselves in time, not because of any lack of quality, but because the central ideas will be increasingly undermined in culture and eventually abandoned. Individual incidents and phrases will be the focal points and take the blame, but it is the values which are hated.
While that process is just beginning, and well before it is complete, I would like to note that in Lewis, and even more in Tolkien, there are different races. They have their own histories, their own abilities and preferences, and their own downfalls. None are as wise as the elves. The weakest and least able of the races, the holbytla, turn out in the end to provide the very few key individuals who rescue them all. All are different but essential, and this is not accomplished in other literature. Hollywood achieves it only with an insulting tokenism. At no point do we believe in Lewis that he is thinking "Well, we must find something good to say about giants, to show how non-prejudiced we are." The differences are central to the story.
They were essentially less racist, not more, than the folks of our age, whatever scraps of the culture they came from we now find unattractive.