Not really. You can be faithfully consistent. At least when the framework of the discussion is motivation.

When you're pushing something that is innately illogical it's kind of fake to call it logically consistent. It's not founded on that in the first place. It's founded on religious faith, or emotion. Logic implies reasoning was used to get there.

If your argument is "I will not be using logic so I am logically consistent. Because not using logic ever is consistent use of logic." Well... you might be right on a technicality but it's kind of avoiding the meat of the issue.