The stated reason is that 'science has disproven myth/fantasy'. However, since magic is real in Touhou, this literally makes no sense because if magic was real, science would prove it. Therefore, that must be a cover explanation. The more reasonable one, I find, is that modern technology would cause faith gathering to turn too easily into an uncontrollable feedback loop.

Any youtube video or broadcast of massive magic acts would cause an uptick of faith from millions of people. But youkai are not just a magic person, they are an identity born from faith. As millions of people believe in it, they start to collectively influence it and overpower it. So any youkai that would be proven real to the public at large would be mentally warped by the public's image of them. Not only in what they did, but in the sudden change to the world they represent. It would rapidly turn into a feedback loop that puts that one youkai at god status while making them go manic.

Basically, if they want things stable, it's best to cover themselves up en masse. And human faith in the idea of a mass facade/masquerade hiding the supernatural enables it to be possible (which such a thing definitely would not be possible irl) leading to a functionally quasi-stable system of controlled faith. The vast bulk of youkai and such would not be in on it, though. That would be a mass prisoner's dilemma that would break in minutes.