How big of a role did Senator John McCain play in banning Martin Luther King Day as a holiday in Arizona 25 years ago?

I don’t know what role, if any he had. It does seem though that, based on the categories you picked for this question that if he did oppose it he was, is a racist and lacking in character.
That seems very narrow minded to me.

My understanding is that he played no role in the decision to not recognize MLK Day in Arizona until 1992, when he supported the ballot proposition in Arizona to officially recognize the federal holiday.

The only measurable MLK Day news for McCain is that he voted against it in Congress in 1983.