Mystics for eons have said, "Reality is an illusion."

I've come to understand that reality is NOT an illusion - that is a verbal absurdity - However the 'reality' we experience most certainly is an illusion, a mental construct we experience in our minds, just as you say.

What we experience isn't reality - that is just an illusion, though it is informed by reality, as filtered through and reconstructed by our sensorial and cognitive mechanisms. What we experience is a perspective of reality. Our physical cognition is a perspective - a human perspective, a personal perspective, etc. - as is our spiritual cognition, which is a VERY different perspective, but I am convinced of the very same Reality.

So why are the mystics so adamant? I'm convinced for one thing it is because much of the ego's stranglehold on identity is founded in it's conviction that the universe is ONLY as it sees it. Looked at this way it explains many things, both about the ego and about spirituality - and thus about non-duality.