This is a silly argument. Clothing is not optional; Kagi is. They are deciding to go without an optional good because they don't like what they spend their money on. I applaud them for it and I like Kagi.
Hence he's on point, as ddg ultimately uses bing under the hood, pretty much all search engines would be out.
A plausible argument could be that you're only using it, not actively giving them money (at least for Google/MS). It'd still call that hypocrisy though, if someone made such an argument.