Should “than,” “like,” and “as” be followed by “who” or “whom”

Before anyone comments that "whom" is not necessary in the English language anymore and that I can just use "who" all the time instead, I'll say that my dialect always uses "whom" immediately after prepositions regardless of register. After words that can be used either as conjunctions or prepositions (such as the ones I listed above), I guess it can go either way? Neither feels more or less natural to me, so I'll have to defer to either prescriptive grammar or coin flipping on this one.

In my dialect, "than", "like", and "as" can be followed by either "me" or "I am." (never just "I," except for that one time I wrote "smarter than I" in a song.)

Edit: if the who/whom is not functioning as a subject or object in another subordinate clause. Example: "You said you're smarter than who/whom?" / ""You worry about people like who/whom?" / "You think you're not as smart as who/whom?"