Jesus put it in very black and white terms. "He who is not with Me is against Me, and he who does not gather with Me scatters abroad." (Matthew 12:30)
At the risk of drawing ire, does this verse suggest that even supreme Deity is capable of committing the logical fallacy of false dichotomy?
No. It means that there are two options. 1) Follow Jesus. 2) Work against Jesus.
In order for Matthew 12:30 not to be a false dichotomy, there must really be no third (other) option, as you rightfully point out.
Jesus is saying the same thing, just in reverse order.
Right next door, used to come up to me at the pub and share drinks then moved to a share house across the road and murdered two women who had lived at that address and knew him. He is also the person who told me how to butcher long pork in comparison to an actual pig and where the best cuts were. Had always thought he was joking until I found out he was arrested. Someone claimed I was his accomplice and I was arrested at work on suspicion but was able to prove by receipts that I was hundreds of miles away on every day he did something. Thankfully I used credit cards for a trail for the accounts department.
