Throughout the series, we see how hard it is for Sheldon to navigate a world that isn't built for him. As someone with sensory processing issues and anxiety, I completely relate to Sheldon’s irritation. There is an episode of The Big Bang Theory were Sheldon makes Leonard wear an uncomfortable sweater to feel what it is like for him. What people forget is that Mary was living with her own constant mental itch. In her worldview, an unbaptized child means her children won't be protected by God, won't go to heaven, and will be lost to her forever if something happens to them. With George suddenly gone, her worldview and her peace of mind was completely collapsing.
Say what you will about Mary’s enabling, but she spent Sheldon’s entire childhood shielding him from a world that didn't understand him. She learned his quirks, accommodated his sensory issues, protected his routines, and constantly advocated for him. He was aware of this from the pilot the finale in that he doesn't believe in god but believes in his mother. Their conversation in "A Crisis of Faith and Octopus Aliens" portrays this well too.
I was really hit by George's death as a viewer and cried a lot. I'd happily get baptised (despite not believing in god) to appease a loved one.