Rule for words/set of words that fit "Others with the same *"?

Solution 1:

The problem is not with the noun/phrase; it is with the preposition.

"Others with the same location", it feels off

It is off. In the commonest contexts, it is "Others in/at/near the same location".

Likewise,

"Others with the same race." should be "Others of the same race."

There are no "rules" in English, there is only guidance; some guidance looks like a rule - it probably isn't.