"So, from your point of view, all topics need no further study which cannot be tested to be true or false."

Not at all. But there is a qualitative difference between matters which we can test and those we cannot. This is why I say I am incompetent to judge these matters.

"As a consequence, all religion needs to be eliminated?"

I would never presume so. For myself, I cannot ascertain the truth of matters I cannot test, so I cannot depend on my grasp of them. I make do with my own sense of right and wrong, having tested my fundamental beliefs in a harrowing process that caused me to abandon confidence in rumors and assumptions, in acculturation I absorbed as a child. This was undertaken at great risk, shattering my religious faith, my affiliations across society, and even my family. When I discovered beliefs I could not support factually, I was compelled to moderate them to suspicions, and those I was able to falsify I had to abandon.

For me, I was unable to say I believed in claims I found factually insuperable, and this included religion. I can only make such statements for me, and I have repeatedly pointed out my reticence to challenge others' beliefs, because of how harrowing that process was for me. As for what replaced it, I have pointed that out also, that I no longer have certainty about anything. The best I can arrive at is that things that have been tested and not disproved are potentially true, at least until better understanding falsifies them in whole or part. This is greatly humbling, and why I say I am incompetent to make such judgments and am lucky to be able to tie my shoes, regarding my intellectual capacity.