Thanks for reading it. Gemini said those cited religions do not commit the Texas Sharpshooter fallacy. But, it agreed that Christianity and Islam does.
I think you got the orientation of the Infinity Religion wrong, though. You only noticed the first layer where everything is true. As one advances up the logic and scientific method ladder, they get better at discernment of truth from contradiction. I, myself, am at level three in this religion. This means I have a good command of fallacies and the scientific method. At this level, two and two is four only.
There's also the fourth level above where I am at, which encompasses axiomatic set theory and logic (logic with the symbols) and the full scientific method. Usually, a Masters degree in a science is enough to bring one to level four, but even then they might still need more math to get to the logic part.
So, the Infinity Religion actually embraces science, math, and logic while providing a framework to bring everyone up.
Hopefully, you have a better appreciation of what I am trying to do now.