In 1 John 5:1 we have John telling us about a present state (believing in Christ) and how we got to this point (we were born of God). The Greek perfect tells us that the being born happened at some time in the past and it has implications into the present (the present of John's writing). The passive tells us that we did not act upon ourselves, but it was God's acting that "born-ed" us again and because of His action we believe in Christ.
So, we are not committing a fallacy here. We are simply reading what the fully nuanced Greek text actually says. It would be the same as reading a police report that says "the suspect pulled the trigger and the gun fired." The gun firing is the direct result of the suspect pulling the trigger. When we come to that conclusion based on reading the report, we cannot make the post hoc fallacy because we are not making a logical leap. Rather, we are reading the facts presented to us as they are presented to us and making the connection that the author intends us to make.
Blessings,
The Archangel
Let me give an illustration that shows my point. Forgive me for the silly illustration, but it's the only way I can think of to reconstruct the language into a similar situation to prove my point.
There is a car that when driven emits a smelly chemical. Driving the car causes the chemical, and exposes the driver. As the car drives, the people standing on the sidewalk are also exposed, which causes them to run away. At the time of the statements below, the exposure has happened in the past, and the people are currently driving & running. I think this mimicks the same language that we're speaking about.
1. All who are driving have been exposed.
2. All who are running have been exposed.
(similar to 'all who are believing have been born')
Now in 1, the driving caused the exposure. In 2, the exposure causes the running. In both, at the time the statements are made, the exposure happened in the past, and the action is ongoing. The same exact grammatical construction can be used to show both causal relationships.
Therefore, even if you are correct about the grammatical construction of 1 John 5:1, we simply cannot use this grammar to show a causal relationship. Sorry, but there are a couple of logical fallacies being used here. First, we can't take a simple assertion and turn it into an If-Then logical condition (the way it's being used here, anyway), and we can't show that "prior to" means "cause of." It just doesn't work that way. Your position very well may be correct, but you can't use 1 John 5:1 to prove it.
Besides, the point of 1 John is assurance. He's simply giving a way for people to be sure that they're saved.
Respectfully