What is usually happening is that other technological or consumer behavior is already leading to the decrease in business of some industry, and the divestment push happens simultaneously (because of people's awareness) and is merely a symptom of their final decline.
Take South Africa in the 80s, or the ridiculous grape boycott of the 90s, etc. None of those symbolic acts led to actual changes happening -- those were all consumer or political changes already in flight.
People create much more effect by voting with their dollars than by symbolically calling for divestment. It usually turns out that there is someone willing to take your place as a buyer when you choose to divest. It's only through fundamental change in demand or supply that a business is affected. Stop believing in the effectiveness of the feel-good boycotts. Even Blackrock won't make a difference.