Can I stay friends with my friend's ex without making her feel I've chosen him?

My friend saw a photo of me and her ex at tennis and wrote, "I didn't realise you two were still making plans." They split up two months ago. She introduced us, and we'd been playing together long before the breakup.

She says the split was mutual, but seeing him in my ordinary week makes it feel as if nothing has changed for anyone except her. I hadn't thought of that. I'd avoided mentioning her at tennis and thought keeping the friendships separate was being considerate.

Now she says she isn't telling me whom to see, but would rather not hear about him. I can do that. I also don't want to start lying if she asks what I've been doing, or use her wording as permission to ignore how hurt she looked.

How do I keep both friendships honestly? I'm not asking her to socialise with him; I just don't know how much information to offer when saying too much and saying nothing both seem loaded.