We have a range of tow bar racks that are designed to allow twin rear doors on a van to open.
The Uebler H Series is available in a 2-bike (H21 Z90) and 3-bike (H31 S90). This rack has a huge 90 degree tilt and a mounting block that is low-profile enough to leave space for the doors to open without catching. For this range the distance from the top of the tow ball to the lower edge of the vehicle door must be at least 40 mm to allow your doors to open.
The Atera Strada EVO RV has been designed slide away from the back of the vehicle (rather than just tilting).
This rack slides far enough to give enough clearance for large vertical tailgates and barn doors to open. This rack is suitable for larger bikes and e-bikes. It takes two bikes and an you can add an adapter that will allow you to take a 3rd bike. The distance from the top of the tow ball to the lower edge of the vehicle door must be at least 50 mm to allow your doors to open.
If you need to carry four bikes the Atera Strada DL3 tow bar rack gives you the most clearance. This rack also slides away from the back of the vehicle (although not quite as far as the Strada EVO RV) so it gives you more space to access the back of the vehicle compared to most racks, although possibly not enough to fully open your back doors.
If you take a look at this diagram, you can see more information on how far out the Strada DL3 rack slides and them compare it with how much clearance is required for your barn doors:
The Atera Genio Pro is a great option for e-bikes and has an extended tilt setting, although this still might not be enough to fully open your rear doors:
Sorry we cannot give you a definitive answer to this question in this case, it will depend on various factors including the type of tow ball you have, the angle at which it is fitted and how wide your handlebars are.