Welcome to the TH community, KCloutier!
I'd recommend you to check the file system of your WD My Passport in Disk Management on your computer. If the HDD is formatted in NTFS (which is the most common file system and what Windows computers use), then you should check if your Smart TV is supporting it. There are a lot of TV models that support ONLY FAT32 file system (which is supported by all computers & devices), but it also comes with some limitations:
http/products.wdc.com/support/kb.ashx?id=MMZnos
If you need to change the file system, then you should know that it will require you to reformat the external WD My Passport and erase all the data on it. So, just make sure you have backed up the movies beforehand. Here's a tutorial...