I'm as far from being religious as you could possibly imagine. I strongly believe the scientific method is the single best tool humanity has to discern reality from misleading inferences our minds tend to make due to confirmation bias and other evolved approximations.
I'm an occasional user of both psychidellics and cannabis.
Far from making me believe bullshit, my experiences with these altered states of consciousness have been not only incredibly beautiful sensory experiences but profoundly fascinating from an intellectual standpoint.
In short, LSD makes you ponder everything. It makes you look at the world around you in a new light. You already know rationally that when you look around you, you aren't directly looking at reality. You're looking at your brain's model of reality. A model generally informed and refined via your senses, but imperfect nonetheless. You don't typically perceive just how imperfect it is, and how arbitrary the mapping of sensory input to emotional experiences really is.
The first time I tripped, my faith in my own mind's model evaporated. I knew the outside reality hadn't changed, but *my* world changed in every way you could possibly imagine, and many ways you could not. Most of this experience is almost impossible to put into words forged by humanity to describe far more everyday experiences, but if you imagine vividly seeing colours you've never seen before, intuitively grasping the motion of objects through multiple dimensions, and feeling emotions you didn't know 'exist', you'll have a slight hint of what it's like.
Your rational mind does not go away. You know when you see a brand new and impossible colour it's not because reality has changed, but because your brain uses colour as an internal label for certain perceptions, and what colour it has chosen to represent the sensation of a particular wavelength of light hitting your retina is totally arbitrary. You cry at how beautiful some of the other contenders were. You realise you could just as easily have been born a different being, who's organs can sense a broader spectrum, and it's fascinating to even imagine how this could 'appear' as an experience. You marvel at the wonder and the beauty of the vast range of sensory experiences you can perceive, and the ones that you as a human cannot, but other life forms possibly can.
What I experienced wasn't a delusion. It was a heightened state of imagination in which I could feel things that would normally be impossible, and ponder the fascinating feats and compromises evolution had to make to map the outside reality to the specific way in which we humans perceive the world. This contemplation, introspection, and abandonment of trust in anything your brain convinces you is real is something I'd more closely associate with science than any other philosophy.