Bridgy won't send webmentions (for Instagram) properly without it, so I'd submit it's more of a webmention issue. It's definitely not a theme issue, and even if it were, only the smallest number of themes would ever be aware to support it anyway.

Given the broader number of users this could potentially affect, it should be sitting some where towards the top of the stack. I'd recommend webmention first, otherwise, perhaps the IndieWeb Plugin itself?