A big -1 to this.

You are asking the whole world to take a hit on both performance and memory use, in order to save Instagram memory.

The PR uses the term "immortal" everywhere. There is only one reference to copy-on-write in a comment. Yet this issue about making object headers immutable.
Immortality and object header immutability are not the same.

If object header immutability is to be a requirement, that needs a PEP.

If it is not requirement, but immortality is, then make the obvious improvement of changing the branchy code

if (!(obj->refcnt & IMMORTAL_BIT)) {
   obj->refcnt++;
}

to the branchless

obj->refcnt += ((obj->refcnt &IMMORTAL_BIT) != 0)

Immortality has advantages because it allows saturating reference counting and thus smaller object headers, but it is not the same as making the object header immutable.