Regarding LSD insights as opposed to religion: things LSD showed me were the same 'tendencies' Aldous Huxley talks about in the 'perennial philosophy', similar to basics of western mysticism this is not about any church or tradition but rather about common values. How certain aspects of spiritual developments seem to work as a common denominator, basically. Huxley may provide classical examples from literature but I get the feeling the core is something often pointed to by practicioners of mysticism.
The way this went for me was: I ate way too many mushrooms at one point, without any previous brainwashing - no deep beliefs... I was raised in a quite free way.
Then with the mushrooms I had certain experiences that were quite extreme. Later on in Buddhist descriptions I found similarities as close as I had ever seen. Zen-buddhism seemed the least indoctrinating to me while still resembling what I had experienced, I discovered the concept of temporary enlightenment.
I cared only about the core of how mysticism seemed to work. For a while I became obsessed with the 'status' of enlightenment but later I realized that it got me nowhere and that anything spiritual I would have to work for starting from scratch. I still think I am nowhere... but that over time, my willingness has grown: I remain open to suggestion.
Like Ismene indicates: human experience stands central. Well that is not only my opinion but also mysticism by definition.
Well ok, nothing about what I said so far is about how to handle your insights...
Ways in which I have changed over the years mostly have to do with lowered thresholds, becoming more sensitive to new ideas or information. There was a time when I felt too open-minded. I lost my critical thinking during that time and compiled ideas trying to stitch together 'what the bleep do we know' type of stuff. Then there was a period in which I discovered healthy skepticism and how to censor my ideas, discerning fantasy from empirical fact. But basically, LSD and other psychedelics helped me become more understanding to others that may come from a different place... and to play more freely in creative context.
About lowered thresholds: I believe psychedelics have promoted a state of
"low latent inhibition".
As is mentioned in the link, something like that increases sensitivity to both things like psychosis or other forms of desintegrated reality perception, but more positively, creativity can benefit from this. The latter is said to be especially true in intelligent individuals. Tests I took when I was 18 have shown that I am gifted, which would qualify me.
To me, these explanations regarding long-term effecs of psychedelics and lowered latent inhibition are consistent.