If you are accused angrily of sexism and misogyny, and you think the accusation is unreasonable, this is what I suggest you avoid at all costs: replying to your accusers.
The reason is that it can be the case that your accusers are skilled with use of language and spin, and any attempt you make to rebut them will be misquoted and distorted, providing them with even more ammunition.
How do I know this? Because I have been there - not because of accusations against me, but against friends. My attempt to defend these friends were futile, and possibly even made things worse.
The response I would suggest is to review what you have said based on the opinions of friends you respect. If you find merit to the criticisms, then admit you were wrong and make corrections, but those corrections should meet the approval of yourself and those whose opinion you trust, not your accusers.
Nothing you do will satisfy some of those who rail against you. So don't try.