I am confused if the embeded clause is a relative clause, not a noun clause.
Ask people which of these four crosses (that or which) they like best.
Hello again, Jiho,
That is not a possible reading. You cannot add "that" or "which" there.
If "they like best" were a relative clause, the sentence would be ungrammatical.
*"Ask people which of them" does not work.
That is what your would-be reading implies. So your would-be reading is wrong.
If you wish to understand the sentence, please refer to my first reply.