Counterargument #1:

If you are god, then the universe allows for "gods" which can arbitrarily alter the state of the universe. Therefore, any utility gains I make have an unknown duration - it's entirely possible that an instant after you grant my utility, you'll take it away. Furthermore, if you are god, you're (a) flipping a coin and (b) requiring a donation, so I strongly suspect you are neither friendly nor omni-benevolent. Therefore, I have no reason to favour "god will help me for $1" over "god will hurt me for $1" - you could just as easily be trying to trap me, and punish anyone who irrationally sends you $1.

1b) I have no reason to select you as a likely god candidate, compared to the ~infinite number of people who exist across all of space-time and all Everett branches.

Counterargument #2:

There are finite many states of "N".

2a) Eventually the universe will succumb to heat death. Entropy means that we can't gain information from the coin flip without approaching this state. 2b) Even if you flip coins incredibly fast and in parallel, I will still eventually die, so we can only count the number of coin flips that happen before then.

Counterargument #3:

Assume a utility function which is finite but unbounded. It cannot handle infinity, and thus your mugging relies on an invalid input (infinite utility), and is discarded as malformed.

3b: Assume that my utility function fails in a universe as arbitrary as the one implied by you being god, since I would have witnessed a proof that state(t+1) does not naturally follow state(t)

Counterargument #4:

Carefully assign p(you are god) = 1/N, where N approaches infinity in such a way as to cancel out the infinite sum you are working with. This seems contrived, but my mind assigns p(you are god) = "bullshit, prove it", and this is about the closest I can come to expressing that mathematically ;)

Counterargument #5:

Assign probabilities by frequency of occurrence. There have been no instances of god yet, so p(god) = 0. Once god has been demonstrated, I can update off of this 0, unlike with Bayesian statistics. My utility function may very well be poorly designed, and I believe this can still allow for FAI research, etc.: social standing, an interest in writing code, peer pressure, etc. all provide motivations even if p(FAI) = 0. One could also assume that even where p(x) = 0, a different function rewards utility for investigating and trying to update even zero-probability events (in which case I'd get some utility from mailing you $1 to satisfy my curiosity, although I suspect not enough to overcome the cost of setting up a PayPal account and losing $1)