Maybe they were interested in nature and environmentalism? Opposed to polluting the environment and knocking down
trees? I think I've heard modern "tree huggers" derided as hippies or neo-hippies, or something.
I think I've heard jokes about the drugs, too. The drugs cause a mind-altering state, a trip, an alternative state of consciousness. Which arguable, reading does too, without the drugs. And
The Lord of the Rings was not like other
books, I gather, much more fantastic than the average book. Maybe it was a heightened trip, doubling down by taking the mind-altering drugs while reading TLotR? Something about there wasn't a sci-fi or fantasy section in bookstores back then, those genres would have been looked at as embarrassing.
Tolkien was a bit of a rebel, but he was a dignified rebel. He swam with the current and didn't scare people. He found a meaningful place that he like within society, and within the
realm of academia he challenged the usual assumptions about storytelling, fantasy, fairy tale literature and he did it in a cordial, good-natured way.
The hippies were probably just seen as rebelling against every thing.
Everything. Maybe Tolkien felt embarrassed about hippies seeming gaudy and undignified, embracing his work and lifting it up. I haven't read Tolkien's biography yet, maybe he felt he had a reputation that was threatened, or thought he had a reputation he needed to preserve.
Just speculating, although it's uninformed speculation and generalizing.