In order to directly invite an opposite faction player to your party, you must right click invite via the social friend list, but because both of these accounts are tied to the same BN account (mine), I am not a friend of myself and I can’t use this method. If you type /invite it says player is unfriendly. I also tried creating custom groups in group finder and the groups could not be found. I have had this issue since cross faction parties were released, and not sure if it’s a bug or just an oversight. I can farm old raids easily with opposite faction friends because they are visible on the social tab, but it’s frustrating I can’t invite myself. If anyone knows a solo workaround, I’d appreciate info.
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I have not done this myself, but what you need is to start a cross-faction community. Then you can invite them directly through your community membership list.
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I can confirm this works. I created a community, went to Community Settings and checked the Cross-Faction option, and then invited an opposite faction character on my other account to the group. After accepting the invite I could click on their character name in the community membership list and successfully invite them to a cross-faction group.
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Thank you both so much! I just tested it out and this is a perfect solution for my issue. 
I’m happy to find out it also works well for my characters on other realms, too. I appreciate you taking the time to respond.
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I still agree with your original point that it should be possible for you to invite opposite faction characters on connected accounts without the whole community workaround. So hopefully Blizzard will find a solution to that.
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