If your job is evangelism and you get to the point where you are claiming in a tweet that your employer "supports" you there is a real risk that you are asking

If your job is evangelism and you get to the point where you are claiming in a tweet that your employer "supports" you there is a real risk that you are asking them to evangelise you rather than the other way round and then your position is likely to be precarious. When you are employed, particularly in a PR or role or any other where you speak for your employer your speech is not fully free. Even when in your own time on private accounts if you claim views and opinions as your own rather than your employer's it can still have an impact. Anonymity is valuable if you have something that you want to say without bringing your employer into the issue. This is not to deny that there may be sexism or that it may be right to publicly stand against it but when in controversial territory speak for yourself and let PR or the CEO back you publicly if they want to and do consider the affect on ability to fulfil role and then balance the need to make a societal impact against that (or quit and speak freely).