If a pro tennis player declined to play in mixed doubles to shield their spouse from paparazzi gossip, would you call them sexist?

What Joe Random would call them isn't so interesting, but the legal question is (can be, I haven't had my coffee yet...)

Not sure if you read the article, but he's more than down to play with women in group settings or public events. It just happens that 1. you tend to banter and joke as you play together 2. due to his popularity, any innocent interaction is clipped and made into a scandalous clickbait for profit by people online.

If anytime someone in an office had a private meeting with the blinds down with a female employee led to accusations of infidelity would you continue having said meetings with the blinds down?

I get what you're trying to say, but your analogy isnt the best imho. It would be more like having the blinds open, and you both get photographed going into the room, and taking of a jacket (oh look, they go in there and undress)

I(male) cannot play with ninja either

Time to raise up against The Man who is holding you down, my friend.