You're making an is-ought distinction. Of course we should not believe serious accusations against someone until they can back up their claims -- in an ideal world. In the real world, standards of evidence are routinely weaponized against decent people by assholes. Everybody knows that Trump has colluded with Russia, but no one can make anything stick.
As another example, there is a small but growing movement to weaken the standards of evidence for rape and sexual assault. These crimes are notoriously difficult to get evidence for that meets the burden of proof, and the result is a very low conviction rape and active harm to women and society by rapists on the loose. I find it increasingly hard to challenge this argument except on theoretical or procedural grounds, and some countries -- such as Spain, which has special violence against women tribunals where the burden of proof is essentially on the accused to prove innocence -- have already followed through with this idea in their laws.
> What harm has he "continually done" to deserve this?
Numerous women have come forward with stories about being sexually harassed by Stallman over the years. He creates what is known in law as a hostile work environment. Women are afraid to work with him because they might be inappropriately propositioned, and risk consequences if they turned him down. (Stallman was "protected" by people in the MIT community, including Marvin Minsky.) And of course, he actually did advocate for legalization of child rape earlier in his career.