I think the difference between EfreetSK's example and the situation to which MLK's quote applies is that MLK already had enough people on his side to force others to take him seriously.

In the UK, demonstrations for trans rights are fairly common. It is also almost exactly as common for them not to be reported on at all in any major news outlet. With the laws in the UK as they are, any trans person participating in a "disruptive" protest is liable to end up in a men's prison (and if self-medding, as many must, deprived of HRT) for a long time, so there aren't many takers for the Just Stop Oil brand of protesting either. It sucks, but sometimes softly softly is what's required.