I find stoicism to be Taoism's spiritual sibling in the West. From the Dao De Jing, passage 5, Red Pine's translation:

"Heaven and Earth are heartless / treating creatures like straw dogs / heartless is the sage / treating people like straw dogs..."

and his translation of one commentary:

"Heaven and Earth aren't partial. They don't kill living things out of cruelty or give them birth out of kindness. We do the same when we make straw dogs to use in sacrifices. We dress them up and put them on the altar, but not because we love them. And when the ceremony is over, we throw them into the street, but not because we hate them. This is how the sage treats the people."

It reflects a detached, broad perspective on the world, which does not deny our very attached and narrow view, but rather augments it and provides a counterweight to our suffering.

There's some passages in the Zhuangzi (another of the 3 central ancient Taoist texts, along with the Tao Te Ching and Liehzi) that feel very analogous. I'm too lazy to find actual translations right now so bear in mind my recollection may be flawed.

There's a part where it talks any how, if you're sailing on a river and an unoccupied boat comes down the river towards you, you simply avoid it. But if that boat were occupied, you might holler at the person to get out of your way, and it might be upsetting.

There's also a passage where Zhuangzi's wife has died, and his friend find him merrily beating a drum. He asks if this is the proper way to mourn his wife. Zhuangzi replies that he had initially cried and lamented when his wife passed, until he realized that she had become what she was before she had lived, and that to everything there was a season. (There's definitely more here than I remember off the top of my head.)

Tangentially, if one has only read the Tao Te Ching, the Zhuangzi and Liehzi are also great and worth reading. The Liehzi is very short, and the Zhuangzi can be abridged to the first 7 chapters if desired. (Chapter 17 slaps but is mostly a reiteration of chapter 1.) You could read all 3 in a weekend (if you abridge Zhuangzi).

Some free audiobooks:

Tao Te Ching: https://www.youtube.com/watch?v=fCLpgXmK3cg [1hr]

Liehzi: https://librivox.org/the-book-of-lieh-tzu-by-lieh-tzu-transl... [3hr]

Zhuangzi abridged: https://www.youtube.com/watch?v=pCQYEeHlXOY [2hr]