In my experience it didn't matter at all, they considered "you work for us, its known you work for us, therefore your opinions reflect on us".
Absolute nonsense, they don't pay me for 24 hours of the day. I told them where they can stick it (politely) and got a new job.
Also a relief to hear that other people had to deal with this nonsense. I was afraid the reaction would be “there’s no way that happened,” since at the time I could hardly believe it either.
Bold and silly of you to even reveal where you work tbh.