I find that individual, personal spiritual experiences are and have been of perhaps primary (bottom line) importance in my religious life - and I suspect that this is the case for many other people; and that it is either lack of such experiences, or a trained disposition to explain-them-away which prevents many intellectuals from becoming religious.
One factor in this may be that such experiences are - and are intended to be - personal - to nourish and sustain individual faith; they are not meant to be quasi-scientific and public arena proofs for use in debate and apologetics.
They are meant to be convincing to the person who experiences them, as a bedrock of their faith - and often they are; but this can be easily subverted by argument and analysis, and the selectivity, exaggeration and distortions - and defensiveness - which creep in when expounding such experiences.
But one thing I had not previously noticed, was that the context and nature of religious experiences forms a hierarchy:
1. Deism - a spiritual experience which implies some intelligent order in the universe, such as might occur in contemplation of nature, or from music or mathematics.
2. Theism - a spiritual experience which implies the reality of a personal God - for example synchronicity (for coincidences to be meaningful to me personally implies that somebody is 'arranging' them).
3. Christian (or other specific religion - mutatis mutandis) - a spiritual experience of Jesus Christ as Lord and Saviour - perhaps when praying, reading the Bible, hearing a sermon.
4. Denomination - a spiritual experience in the context of distinctive features of a particular denomination - for example in the context of Roman Catholic devotions to the Blessed Virgin Mary, Orthodox veneration of icons, or from reading The Book of Mormon.
It may be that a spiritual experience for an atheist is more likely to be Deistic, or Theistic than it is to be a specifically Christian experience- for example C.S. Lewis moved from Deism (a kind of Hegelian idealism), to theism and then only after about a year to Christianity (I don't think he had a spiritual experience which bound him personally to a particular denomination within Christianity) - and my own trajectory was much the same.