When a job ad says the organization prioritizes applications from underrepresented groups (and lists them), should you identify that you are a part of any/some of those groups in your application? What about in the case of disabilities including mental illness?
The problem with self-disclosure even in instances where companies are striving to use more equitable hiring practices, is that employers can appear to, and even believe that they are satisfying their mandate to hire diverse employees while still discriminating by choosing among "preferred” barriers to employment.

My advice has traditionally been this: I don’t disclose anything on a job application or in an interview that can be used against me, especially if it shouldn’t be.
It is illegal in Canada to base a hiring decision on any of the 11 grounds for discrimination identified under the Canadian Human Rights Act unless an employer is specifically working to create opportunities for a group that is marginalized and, as a result, is underrepresented in the work force. With this said, discrimination still happens and for a long time it has been common practice among employment counsellors to advise clients to “not talk about it” in the application to minimize the chances of them being excluded from the interview process. This does not address bigger concerns about systemic inequalities, but does give some job seekers who may otherwise be excluded a chance to get to the interview stage where they have the ability to speak for themselves about their abilities, accomplishments and suitability for the position.
The welcome trend among many companies to diversify their staff, however, complicates what has traditionally been an undisputed rule of the employment service world. In fact, when applying to organizations that have equitable hiring policies Jacq Bass of the Rainbow Youth Coalition of Yellowknife says, “It's pretty standard to list affirmative action categories that you self-identify with in a cover letter.” There are also specific government programs that provide employers incentives if they hire individuals with disabilities and other barriers to employment. As a result, the advice I give now is a little more nuanced.
If an organization is known to have a very inclusive hiring practice and asks people to self-identify so that special consideration can be given to marginalized groups, a person may want to disclose. With this said, it has still been my experience that even the most progressive employers can have internalized biases when dealing with certain barriers. Mental illness, for example, carries with it a well-documented stigma that can be quite pervasive. The question then becomes one of how to identify?
In some cases, being direct makes sense. A person might choose to state, for example, “I identify as a racialized woman,” or “I have lived experience navigating community and social services as a person in precarious housing.” This makes sense if you are applying to an organization whose mandate is to serve this group. In other cases, being more general by specifying that you would like to be considered for an equity hire might make more sense. For example, you could write, “I identify as a member of a marginalized group, I would like to be considered according to your equity hiring procedure.” Choosing to be strategic in your language is an effective way to make a disclosure of this kind without raising concerns that shouldn’t be there to begin with.
With all of this said, whatever identification you choose to make, the one old piece of advice that still holds true is this: focus on your strengths in the application. An employer with an affirmative action policy will likely hire a person with a disability, but won't hire a person with a disability if they believe that disability will affect that person’s ability to perform the job. In my experience, being confident about your abilities is, in the end, the best way to combat these concerns.