This ptototransistor specifies 100 nA for Collector Dark Current. And you are probably not completely covering the sides and all. Modern LEDs are stupid efficient and might be visible even at that current. And I would not be too concerned by this extra consumption.
I run all my indication LEDs for indoor use at single uA typically and this is plenty for stuff on the development boards. They are blinding otherwise.
Look with the scope at the RX/TX lines and see what exactly fails. You may be touching some pins while covering it and inducting some noise or something like this. I don't see why this would not work.
And for a cleaner test, just remove the transistor on one of the board and see if you still have an issue.