As the patch in [1] targeting the execution of the plan in ExecutePlan depending on the destination was declined, I hacked around a bit to find another way to use parallel mode with SQL prepared statements while disabling the parallel execution in case of an non read-only execution. For this I used the already present test for an existing intoClause in ExecuteQuery to set the parallelModeNeeded flag of the prepared statement. This results in a non parallel execution of the parallel plan, as we see with a non-zero fetch count used with the extended query protocol. Despite this patch seem to work in my tests, I'm by no means confident this being a proper way of handling the situation in question.
Best
Tobias
[1] https://www.postgresql.org/message-id/CAA4eK1KxiYm8F9Pe9xvqzoZocK43w%3DTRPUNHZpe_iOjF%3Dr%2B_Vw%40mail.gmail.com