I didn't find any of those tweets unprofessional. I found them to be a genuinely interesting perspective on social issues that I am interested in. I am not sure how that's unprofessional of her.

If you think its "leftist nonsense", then that's just your opinion.

She is entitled to tweet whatever she wants to from her personal twitter account. Do you think its reasonable for her to follow your idea of how a Director of Engineering should tweet?