Roberts said in her book; The Experience of No Self, the moment this happened it felt like a great blowing out, an intense outward leap of the "living flame within". She felt the awesome presence of God, like a feeling of ecstasy. However, after this union with God both the experience of God and the experience of self fell away. In her words, after that blowing out, the world seems "dull" in comparison.
What I got out of reading her book, is that most people's experience of God, the common way that they "feel" God's presence, is really the sense of their desire for God; but not God itself (ding an sich). When our sense of self vanishes, so to does God the concept, the thing of which we desire, dissipate. As a Christian, this was her interpretation of the events. And I'd recommend reading her book, though it is a very rare find indeed.
Buddhists report something very similar when they reach Enlightenment; and so to do Hindus. In fact, Siddhartha Gautama (the Buddha) described his experience under the Bodhi tree in a very similar way as Roberts' attainment of No-Self. It's not a coincidence that mystics in general, of all religions, experience the same thing but refer to it with different words.
When these individual people describe this universal experience, which Sigmund Freud called "the oceanic feeling", they can only describe it in the religion and culture that they are familiar with.
Bernadette Roberts was a Catholic nun, and Siddhartha came out of Hinduism and was starting something different.
Our minds are limited only to the symbols and language it has at its disposal to make sense of the world around it and what it is perceiving. It can only compare its experiences with what it already knows.
I don't care if you're an Apologist, a Flat Earther, a scientist, a Protestant or Catholic, Muslim cleric, or Hindu shaman. We all operate with the same mechanism inside our brain.
We sense side effects of the world around us (light, sound, etc.) and we interpret these things against what we already know.
If it's agreeable, it is incorporated into our system of knowledge. And if not, we either find ways to work around the information in order to continue believing what we believe, or we might change our beliefs, or we'll simply pass it off as nonsense.
This is, of course, unavoidable, but it helps to know that this process is always going on. Our mind is the great Editor; continuously dropping inconsistencies in order to have things fit together.
While stilling the mind and the ego is something that only a few people have done, even these people can only interpret that experience from their own frame of reference.
What is the significance of this? It means that while we can share the same experiences in any religion, we cannot help but interpret that experience as meaning something that confirms our beliefs.