I am sure that this link created some fun conversations, as I can see it doing for this post as well.
I think that your question is valid, but I have concerns. We are using words that have 'dictionary definitions' and connotations. Since everyone will not agree on the meaning of "religion" and "mythology", we start with bias even before we start answering the question.
I see how this has a specific application towards religion, but it may serve us better to say, " You need to consider the possibility your worldview is false."
Yeah, I like that. Many don't even know what "worldview" means so they don't get triggered when someone questions it. Many many not realize their religion is their worldview and impacts most major aspects of their lives in terms of how they view themselves, the world they live in, their purpose, morality, ethics, virtue, meaning, the future, what happens after they die, etc, etc.
I would definitely be the first to attempt that my faith has a major impact on my worldview, so I am not able to detach the two. Some people don't realize it. And still, others are zealous in defending their worldview even though it is not based on religion.
My time spent overseas (over 10 years) helped me take a step back to examine my worldview as I was interacting with people who had a very different one than mine. Some of my views changed. Some were strengthened.
Appreciate the conversations you are helping people have!