So as someone in the tech industry, it wasn’t just morally right, it was entirely necessary.
With his memo, Damore made it clear that he’s not a good faith actor in the system. It would be impossible to allow him to do performance reviews of peers or subordinates because his bias was so egregious. If we were to pretend his memo were about Jewish people or black people, it would be a little more obvious.
It inherently limited his ability to work on a team; women were already saying they would to refuse to work with him (turns out Google employees maintain blacklists of people they won’t work with). The situation was entirely untenable.
Perhaps you could make the point that it was better that he was OPEN with his biases rather than keeping them hidden, but the show of impartiality when making decisions is really important to the smooth functioning of a corporation.
His document was poorly researched and badly presented. He wasn’t really trying to reform Google’s culture so much as cover his opinion of women with a weak attempt at CLAIMING he was trying to make things better. (His interviews and tweets subsequent to being fired make it a lot more clear that he thinks that any attempt at managing diversity is a waste of time.)
So in the end, it was both morally and operationally necessary to fire him. The only question is whether Google should’ve done it faster, and before this all went super-public.