The sit-ins were specifically targeted to break the laws they wanted changed. I don’t think many people are protesting laws saying that you can’t stand in the middle of the road.
While at a high enough level of disruption, the acts of protesters might harm public support of the cause, I think that level is probably pretty high and supporters will largely understand if they are temporarily inconvenienced, while some people who already oppose the protestor's cause will tend to use any inconvenience as a more socially acceptable excuse to justify their opposition instead of more honest reasons like plain old bigotry.