There will never be a consensus on what it means to “be’ Indigenous or what the qualifications are for someone to claim that they identify as Indigenous. So when we consult “members of the Indigenous community” who are we talking about?
That is the crux of the problem, isn't it? In other areas like sexual orientation or gender identity, there's a decently broad consensus that we should allow people to self-identify. The benefit of self-identification is that it discourages gatekeeping. One downside is that it doesn't change the fact that the broader community may still reject a person's self-identity. See for example the debate surrounding trans women in sports.
The issue becomes more acute when being perceived as a certain identity comes with some privileges, whether informal or sanctioned by our government. When that happens, it creates an incentive for people to self-identify in a way that they believe will benefit them in some way or another.
I don't have a solution. Just rambling.
Another issue is that self-identifying in a certain way shouldn't come with monetary, social or professional benefits. Easier said than done, of course, but at least in some cases it already happens. For example, people aren't entitled to use a handicapped parking spot by merely self-identifying as having limited mobility; sports organizations have (still evolving) rules for trans athletes; etc.
Whatever we do there will always be people who try to take advantage of the system, and people who will unfortunately fall through the cracks. Part of the issue is also that many of these identities aren't binary: plenty of people have mixed heritage, or have partial disabilities. What do we do about that, and where do we draw the line? Can we have the nuance to cope with gray areas on a case by case basis? A broad consensus will be difficult to achieve in gray cases.