Devices messed up after connecting another USB drive

I have just installed the brandnew Ubuntu Mate 19.10, amd64 - and I like it a lot. However as of now the system will be unusable for me because:
whenever I plug an external drive to a USB port (can be a stick, can be a hd) the OS will change the order of /dev/sdx's. I.e. my root mountpoint is /dev/sdb1, but when I connect the USB thingie it will become /dev/sdc1 and the just plugged in device will be partition /dev/sdb1. Obviously the OS is hence unable to find any file in the path, so I cannot "ls", "shutdown", ... Only a hard reset will do.
This happens after booting the live image from USB as well as in the installed system. Did anybody come across a similar issue?
For now I shall try to work-around the problem with "gsettings" -automount options ...

I did:
gsettings set org.mate.media-handling automount false
gsettings set org.mate.media-handling automount-open false
gsettings set org.gnome.desktop.media-handling automount false
gsettings list-recursively org.mate.media-handling
and it didn't help: as soon as I plug in an external USB drive the system will not find it's root device no more. I'll give up on it for now ....

apt provided a new kernel this afternoon: vmlinuz-5.3.0-19-generic (as opposed to the originally installed vmlinuz-5.3.0-18-generic). This solved the problem described above.
I wonder why nobody else came across the issue, because it's not unusual to connect an external device during the live session.

Glad a kernel update fixed the issue, but it could be specific to your hardware as the kernel is responsible for this sort of stuff.

I've never witnessed what you've described where drive letters changed (especially for a mounted drive!) after the system was booted, whether it was a live session or installed.

I've only known one system to put drive letters in a different order if I booted with a USB storage plugged in - but this only impacted the auto mount options for a data partition I had configured at the time.

the desktop computer I use is at least 4 years old and, I'd say, couldn't be more generic (all Intel). Here's some stuff from dmesg:
Kernel command line: BOOT_IMAGE=/boot/vmlinuz-5.3.0-19-generic root=UUID=5cad6196-b2fa-4875-9157-cceafd9b24c1 ro splash acpi=strict loglevel=3 vt.default_utf8=1 apic=verbose vt.handoff=7
...
smpboot: CPU0: Intel(R) Core(TM) i5-2500K CPU @ 3.30GHz (family: 0x6, model: 0x2a, stepping: 0x7)
...
fb0: switching to inteldrmfb from VESA VGA
...
i915 0000:00:02.0: vgaarb: changed VGA decodes: olddecodes=io+mem,decodes=io+mem:owns=io+mem
...
usb usb1: New USB device found, idVendor=1d6b, idProduct=0002, bcdDevice= 5.03
...
I might test the original ISO with 5.3.0-18 -kernel on another machine, however I am quite happy for now with 5.3.0-19 (and hopefully with todays 5.3.0-23).

Thanks a lot for the comment lah7!