The practical obstruction is if you block the browser API access, they test for it, and then block you so you can't view their site, and they do that by using the information that you leaked.
As for the effectiveness of blocking what they are doing, you can block them by giving them bogus but plausible data. There's a range of accepted values for those interfaces. If its within that range, they can't tell the difference, but their entire assumption is its determinate, when it can never be determinate because a hash is a finite field.
Their assumption is based on applied probability which has validity issues in an adversarial environment.
As for the effectiveness of blocking what they are doing, you can block them by giving them bogus but plausible data. There's a range of accepted values for those interfaces. If its within that range, they can't tell the difference, but their entire assumption is its determinate, when it can never be determinate because a hash is a finite field.
Their assumption is based on applied probability which has validity issues in an adversarial environment.
Neither requires solving the halting problem.