Firms want to bring more diverse candidates into their business. Evidence shows time and time again that it will improve a business, both in terms of the working environment but put as crudely as possible, will also result it better revenue. All the time clients are asking them to provide how diverse they are as an organisation, there will be these form of mentoring programmes to help support and bring certain under represented groups through the process.
To me, the above says that they will basically keep an eye out for your application. If it is below the standard they would look for, you won’t get through - it’s not like prioritisation means you get to bypass any set criteria. It just means your application is likely to be flagged earlier and brought through any stages earlier too. In any borderline decisions or where they have too many candidates going through to the next stage, then you might be prioritised over another candidate, where you have a connection to the firm.
The difference these mentoring programmes have is not in how your application is reviewed. It is just giving you more opportunities to ensure your application will meet the standards the firm sets.