Then-Pope Benedict found Mueller objective enough to appoint him to that position. In any event, the SSPX has criticized Pope Francis more than they criticized Abp Mueller, so it’s unlikely they would consider Pope Francis “objective” either, and he oversees the process.
Over the last 40 years there have been a few administrators of the CDF, and other relevant Vatican offices, from different continents, different kinds of theological education or emphases. Were they all biased?
This is the same process as the local level; the SSPX chapel agrees with the “office” of Bishop (but not the man who currently holds that office in our city). They regard his predecessors since 1972, who had backgrounds very different from each other, as also biased. The SSPX affirms the papacy - in theory - but regard Pope Francis’ teaching as reflecting only his opinion, not the Papacy, itself.
To paraphrase Chesterton, I don’t need a Church that’s right when I am right, I need a Church that’s right when I’m wrong. Maybe the solution is not waiting for a future, “objective” CDF administrator, or a future, “objective” pope, or bishop, or whatever. Maybe the solution is conversion, in the present. Some individuals have taken that step toward “regularization” already. The Church won’t be a perfect fit for them - it isn’t a perfect fit for anyone. It’s not supposed to be.