Striking down believers with lightning is, obviously, counterproductive: at the least, the Church of Thor Triumphant would get a boost in attendance.
The best strategy I can think of is to make the lives of obvious believers miserable, but in ways which can be ascribed to bad luck, rather than divine intervention. Then those claiming public virtue will not be able to claim that their belief has made their lives better.
Let the Pope suffer a series of strokes. Let the Dalai Lama contract facial cancer which somehow resists treatment and disfigures him. Multiply this sort of thing as necessary. Call it the Job approach, without the final reconciliation.
Even better, since many people (including religious leaders) have public virtue but private failings, the aGod could boost their careers and then, when they gain prominence, arrange for their private sins to be revealed. Think of it as the Jimmy Bakker strategy. A constant succession of discredited religious leaders would probably have some effect.
And "he can't mess with their minds. He can mess with the world" allows some really sneaky loopholes. Can the aGod introduce small amounts of alcohol into a person's bloodstream? Being intoxicated is notorious for impairing judgement. How about a few micrograms of LSD or a few milligrams of mescaline? Uncontrollable visions, anyone? If not direct introduction, why not (with godlike stealth) introduce something like LSD into a person's food? A few hundred micrograms is all it takes. This sort of thing would probably be particularly effective when dealing with fundamentalist preachers of all stripes, particularly Christian and Moslem. In the short term it would encourage sects to become more and more bizarre, but with a little luck (and discreet nudges from the aGod) such groups would self-destruct when their craziness goes too far. Call this one (at its extreme) the Jim Jones strategy.
Buddhists would be a very hard nut to crack, assuming the aGod doesn't like Buddhists, but that may be just a reflection of my cultural ignorance, and real Buddhists might want to weigh in.