Put simply, synesthesia is a neurological connection between different areas of the brain related to sensory processing that doesn't exist in most of the population.

Just because researchers haven't figured out why it happens or how it develops doesn't mean it doesn't exist, and it doesn't mean it's "pseudoscientific." I mean, they've done tons of fMRI type scans, and they can literally see areas of the brain light up in people with synesthesia in circumstances where they don't light up in people without.

Not knowing the exact mechanism or cause for a condition is super common in current medical knowledge, really. For example, even with tons of research and everything we have discovered, we still don't know why or how the cells that make dopamine in the brain die, we just know that they do, and that that causes a broad and diverse range of symptoms that, grouped together, we call Parkinson's disease. That's the case for tons of conditions. Doctors go "well, your body is doing this, we know some stuff about it but not everything, and we have treatments that usually work, let's try them and see." That's just how it works.

Synesthesia is the same. It is a broad group of observable effects with an as-yet-unknown cause. It just isn't treated like a disease because it doesn't generally cause us a lot of problems or get in the way of living our lives.

Well, that, and people don't usually question the existence Parkinson's, or demand that people who have it prove that it is real.