MCU stuff: sell them as development boards. User is responsible for any interference they generate with it, no guarantees of operation, etc. etc.
A trivial exception would be if your device can have wires attached to it, which are driven by the MCU inside, which is programmed with user code. User attaches a long wire. User sets wire to buzz at the clock frequency. User now transmits considerable EMI. What can you do about that? Absolutely nothing. So you can't get approval on something like that. Or at least, it wouldn't be very meaningful if you did; or might be a bit disingenuous to say you did.
Likewise, programming adapters, probably various kinds of communication adapters / interfaces: lab equipment, to be used by authorized personnel in a laboratory environment. May create interference, may be highly susceptible; no way around it, some things just are that way. (Riddle: how in the hell could you get (conventional) CE approval for, say, a lightning generator?

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Anything that you can get (conventional) approvals for, likely should. Yes, it will be expensive.
Some items may have other controlling standards -- unrelated, but similar in spirit. The full and proper USB trademark requires licensing from the USB Implementers Forum, which may include performance and fitness standards, I'm not sure. These will be parallel to -- but distinct from -- CE approval. I would imagine compliance with any such standards will help CE approval as well -- that is, if the standard says you need a shielded cable with insulation covering it, and CE says your shielded cables need insulation over them, well, there you go, right.
What did the distributors say you need to do? Do that. If they can't be very specific (e.g., it needs "CE", but there are numerous ways you could apply that, including by exemption), then drill into the standards they're asking for. Granted, the scope of "CE" is pretty damn broad, so that could take a lot of drilling. (Perhaps this is precisely the point you've reached, and need to know more about CE to go further?)
Tim