[Update:] This answer refers to the initial version of Bill's arguments in the comments. By the time I had posted this, Bill had already made a less extreme point about tweaking colour rendering rather than turning it off. I don't have enough experience with that to weigh in on the difference of opinion between Bill and Asaf about whether this would be an efficient solution of the problem.
I'm disappointed that four people downvoted this question, most of them apparently without making any constructive suggestions. All the more so because Asaf was merely alerting us to a problem and making a reasonable appeal to consider alternatives, not asking anyone not to use colours. If, as Phira suggests, people downvoted because they have trouble reading stuff emphasized by bold/italic/underline instead, then they should say so, so that we can find the best solution for everyone. So far, no-one has said so, and as long as no-one does, Asaf's suggestion seems like a good solution to me. I doubt that forcing monochrome rendering, as Bill suggested, is a solution, since it would turn off all colours, including in graphs etc., where content might not make sense without them, e.g. in this answer I gave today. I also don't see any contradiction between Bill's announcement that he will use colours when they "greatly aid discerning structure" and Asaf's appeal to consider alternatives, if "greatly aid" is interpreted as "aid more greatly than the alternatives without colour".
So I would ask everyone to take Asaf's appeal seriously, and then if you've considered the alternatives and still feel that those who can discern colours would benefit significantly more from your post if you add them, then by all means add them.