Very hard to know what's going on there from just that screenshot. What application are you using to view the file? On what platform, and what OS? Can you share a sample file with us?
It sounds like LibreOffice is creating a flattened version of the fields, with the drop-down arrow as just an image. I would recommend you remove all the fields from the file before converting it to a PDF, as you'll probably need to re-create them anyway.
But unless you can share a file that demonstrates this issue I can't help you further, I'm afraid.