My Dad was a fanatical camera buff, obnoxiously so . He brought his camera equipment everywhere, including to my cousins' wedding . They certainly wouldn't have kicked him out. He was their beloved uncle and they knew how much he loved taking pictures, obnoxiously so. The wedding photographer, of course, was not pleased.
Turns out it was a lucky thing my Dad was so obnoxious about being an amateur photographer because the professional photographer's pictures turned out like....one of the words we ban here. My cousins were grateful that they did end up with plenty of good photos, thanks to my photo bug Dad.
I would give your dad a pass: a guest who is over-enthusiastic about their own hobby [I can imagine foodies trying to identify ingredients in the menu, and fashion designers/florists "ooh"ing over the dress/flowers also seeming a little OTT] is still a
guest. "Guest Saves Day" is a great memory for the couple to laugh about [when all the upset has vanished], but I'm not sure someone else's professional photographer would hand over their work as a kindness.
A photographer brought along by a guest is an uninvited guest at best, an interloper by any standards, and possibly an unmitigated nuisance/obtrusive interruption to proceedings if they (photographer) don't have the sense to stay in the background.
Influencer? Well, it's making my eye tic a little thinking about how I would handle this [scary eyes/ice-cold politeness is my Level 1 thought, and it doesn't get better from there].