As a client connected to the host, pickup/drop locations do not follow rotation properly.
The link shows me rotating the inserter with identical config.

https://imgur.com/a/leJnslb

I'm not sure what you mean sorry. Can you give me more detail please? Step by step is good. What happened and what you expected to happen. Also if you can reproduce it. And if you can, what steps would I need to do to reproduce the issue?

So w/o changing the inserter drop/pickup config, just rotating an inserter. Just tested in a SP save. Might be related to the vanilla inserter change. Grabbed a video for a better example. https://imgur.com/a/zpkO4nn

I must also add this screws with blueprints where inserters are not North/South orientated.

Same is happening for me today, yesterday it was okay. Copying (Ctrl+C) an inserter with any configuration of rotation reverts it to a vanilla north-facing inserter upon pasting. Exception: if the original inserters target was south, it gets replaces with a vanilla south-facing inserter.
This also applies to Blueprints and the pipette Q. Basically meaning that every inserter has to be adjusted after it is placed.
Shift+RMB and Shift+LMB to copy settings is not affected.

Fixed in v1.3.2