Eevee has severe frame-rate drops with animated objects that have normal maps on them. The problem has been reported and can be viewed with a nice sample file here:
https://developer.blender.org/T64458
This Addon replaces Normal Map Nodes in Blender to improve EEVEE Viewport Performance. The performance gains are significant.
Install the addon, go to the Shader Editor and extend its Tool Bar.
You will see two buttons, aptly named after the setups they will toggle.
Normal will give you the regular Normal Map Setup
Custom will replace the existing Normal Map Nodes with the Custom Setup to speed up the Viewport. Switch this back to regular for rendering.
You will see this Node Group replacing the Normal Map Node
This is based on this idea by pcanback: https://blenderartists.org/t/way-faster-normal-map-node-for-realtime-animation-playback-with-tangent-space-normals/1175379
I am only maintaining this add-on, the heavy lifting was done by anonymous persons and BeheadedKamikaze https://github.com/BeheadedKamikaze
Now contains the necessary fixes to make it 2.83 compatible, graciously provided by Xavier Cho https://github.com/mysticfall . Many thanks for these!
Tested in 3.0. Works just fine.
Compatibility with 4.0 added, graciously provided by Mustard https://github.com/Mustard2, this will break compatibility with 2.8 through 3.0. If you need the addon for these Blender versions, you can get it from the according branch.
Please note also, that if you have a file that still has normal groups from an older version in it, those will break the newer script. Please convert those back to regular normal nodes in your older blender version and save the file for transfer to a newer one.