The key is to make your culture filter not cause people who actually would be a good fit to self-filter. Mental illness is insidious because it can make people who actually would enjoy something if given the right push instead think/assume that they don't want to do it. It affects a large enough percentage of the population that it's something companies need to be thinking about.
One of my friends worked for a company where one of the official values was "100%", and to me this was problematic because different people would understand it to mean different things. Some would assume that it just means that everyone works hard, that it's not a cushy job. Whilst others would interpret it to mean that everyone works crazy hours and is expected to give their life to the business at the expense of other commitments. My friend couldn't recognise that different people would interpret the value differently, so believed it was a perfectly reasonable way to get the wrong kinds of candidates to self-filter.
Every company is different and attracts different kinds of employees for various reasons.
Anti-discrimination is important, but it shouldn't go too far.