Hitting spiders with smite-sword won't deal extra damages for they're not undead. But hitting them with sweep attack seems to be able to deal extra damages.
Bane of Arthropods works that way likewise. Sweep attack seems to deal extra damages to non-arthropod mobs. Is it intended?
Thank you for your report!
We're tracking this issue in MC-117361, so this ticket is being resolved and linked as a duplicate.
If you would like to add a vote and any extra information to the main ticket it would be appreciated.
If you haven't already, you might like to make use of the search feature to see if the issue has already been mentioned.
Quick Links:
📓 Bug Tracker Guidelines – 💬 Community Support – 📧 Mojang Support
📓 Project Summary – ✍️ Feedback and Suggestions – 📖 Game Wiki