Is religious experience the same as objectively verifiable scientific experience? Of course not!
The view that I would endorse says that religious experience is subjective, not objective. The difference is that many people can simultaneously verify an objective statement, whereas a subjective statement can only be "verified" or stated by the individual making the statement.
All of us can verify the boiling point of water, but only I can verify that I have a pain in my toe, or how I feel about abortion, yet in all these cases we commonly might call such beliefs "true" or "false".
What "truth" is can be complicated, obviously but I think, in a general way a pragmatic view of truth works best, and there is a reason for that.
In fact, in all cases "what works best" is a pretty good definition of truth generally speaking. A moral principle can be said to be true because it "works best for humanity" just as a scientific principle can be said to be true if it works better than the other hypotheses.
Planes fly better with wings than without, aspirin works better for a headache than rat poison. But if you want to kill rats, aspirin probably doesn't work at all.
All of these are objectively verifiable. We can line up 500 rats and everyone can observe how well they live with rat poison in their systems as opposed to aspirin. Everyone can see which works "better".
Note that in each case, we are finding what works better for a specific purpose. Hammers are not very good for taking small nuts off of small bolts.
The test for religious views are what works best to give us what we go to religion to accomplish. Most people turn to religion to seek solace, to give their lives meaning, to find their place in the universe, to decide if God exists, or if one should worship a higher power.
But those answers- what gives one's life meaning and peace for example, cannot be objectively verified. I cannot see what gives YOU peace. That is what testimony is for. That does not mean that statements about what gives one peace cannot be "true"- just that only you can know what beliefs work best for you.
Essentially what we do as Mormons and what happens in Alma 32 is that we ask others to "taste this and see if you like it". As it says in that scripture, if we try it and if we like it, and it becomes "sweet" to us, we will follow that path.
Obviously we know there are many reasons people do not follow up on the path, but it is our belief that though people may find something that works for them, we believe that our path works better than any other if they would just follow it and taste its results.
So I don't know if you call that "relativism' or not. I call it "Pragmatism". I think that the truth is found in what works best for its given purpose.
That's it in a very small nutshell!