Hi there Wicket. I don't think you're being unreasonable at all, and I think it's good that you want to challenge the spread of intolerant or racist views - I genuinely believe we need to do this because social media is awash with some pretty troubling statements, images, etc. and if not challenged then they become normalised.
He's clearly a close family member who you really care about, so you're understandably disappointed too. If he's a teenager, this might be a good opportunity to talk to him about in an appropriate way.
I recently saw my DH's 13yr old neice "like" some awful pictures on FB, discussed it with DH and he spoke to her parents about it. They were a bit embarassed, but used it as an opportunity to talk to her about social media, protecting herself from dangerous/violent/offensive images, groups etc. She was embarassed too, but I'm glad we said something because her parents weren't giving her any advice or guidance, which she clearly needed.
Whatever age he is though, he's unlikely to get it simply by being de-friended. And he may well get defensive if he feels you're having a go. But if you sensitively (and privately) tell him you were shocked by the post, and open a conversation about it, you might just get through to him. It might be an opportunity to challenge any misinformed views he has, as well as make him realise that some of his other friends may have been really hurt by the post.
Well done for not just glossing over it though - we need the next generation to build bridges, not create more divisions in our communities.