If you had a dream, this would be real in the sense of neurons firing to create an internally induced sensory experience with specific details. Everyone has had dreams so this is real. Although this is real, there would be no way you could prove the details of that dream, scientifically.
Also, since dreams come and go and constantly change, there would be no way to repeat this dream in all the same details for a repeatable scientific experiment. Therefore according to the scientific method, what was real in all its details cannot be proven. This is due to the limitation of the scientific method and not the limitation of the dream or dreamer.
If you had that dream and knew you had it, it does not matter if science can't see this internal expression. This is beyond its capacity at this time. To the outsider, your hanging onto that which cannot be proven, scientifically, would appear to be based on faith. But is was based on a real experience, beyond science to confirm.
There are things of the mind that can only be perceived within the first person, which do not perform, ideally, for the scientific third person.
If religious experiences occurred within the same neural matrix as dreams, like the details of dreams, we cannot prove this with science as we know. The scientific method was not designed for this type of data. It was designed for things outside the mind. Maybe we need to upgrade the scientific method or add a disclaimer that says certain things are beyond the current method. There is an entire frontier of data beyond the current scientific method. What would need to change is the third person scientist would need also experience in the first person; scientist and experiment at the same time.
A good analogy is studying toothache pain. You can do this from the third person, as an observer, but something would be missing. If you could have a tooth drilled so you had the pain, while also observing the phenomena in question, you would take the science further, than the safety of third person. The scientific method does not do first and third at the same time, because it is too hard. Third person is easier.