I assume you mean by faith in science you are essentially referring to the idea that without having done so, you will be able to duplicate the scientific methodology, and you are going to take a leap of faith in order to test the theory. Just because you are imagining a cathode collecting hydrogen bubbles and an anode collecting oxygen bubbles doesn't make the faith itself distinguishable from faith in anything else.
They are not the same.
One has perfectly logical explanations of how electricity can split oxygen from hydrogen. It is part of a coherent theory of chemistry.
There is ample evidence from multiple sources and can be explained without an in-person demonstration.
The other very important point is that science, based on inductive reasoning, has very specific limitations.
These limitations mitigate the confidence of the results. This confidence is Quantifiable. It's called "Sigma" and it NEVER REACHES 100%.
Now, if I read in some old book that I could turn lead into gold with some unicorn tears and a squirt of dragon blood, and I went around teaching this to people because I 100% believed it, that would be much more similar to a religious belief.
The other point I'd like to make is that the cathode collecting hydrogen bubbles IS TESTABLE (FALSIFIABLE).
The tenents of religion taken "by faith" are NOT TESTABLE (UNFALSIFIABLE).