Respectfully disagree. You're essentially arguing that they're not politically motivated in staying at/leaving their job. That's fair. Nevertheless their actions translate either support, inaction, or opposition. The implication which MLK argues is that inaction is harmful to the movement.
You are taking a consequentialist stance, deciding that if something has political consequences, then it is political. But literally anything could have political consequences. A solar flare could have political consequences. A fly landing on someone's hair could have political consequences. This does not mean that flies are political!
If everything is political, then the moniker "political" is meaningless.
