Can't read/write via `dd`: got /dev/disk2: Permission denied (to Physical device)
I realize that exactly the same setup is working on other MacBooks and even with another admin user on this laptop. So no matter, what kind o issue it is: I think it's something related to my personal setup and setting, not to the system in general. So I will close this question for now.
If someone get the same problem: try to do the same steps as I  described above or in the end: change the machine or user on your one if there is a chance to do this.

make sure that diskX is unmounted via diskutil unmountDisk and diskutil unmount
Change USB ports
if it's SD card: blow with air into the slot (many people said because of the physical lock sensor of sd card.
make sure, that you work via sudo. (just in case, you can check it via which sudo command)