Answer

It is hard for me to think of such a case, and therefore hard to think of sources that would decide it. Still, I will say a few things.

1. The question also applies to testimony, not only to judges. Can a witness testify about something that will indirectly affect him as well? For example, a witness who testifies that a woman’s husband died might be disqualified because perhaps he wants to marry her.
2. So long as we have not found a disqualification, there is no disqualification. Every witness or judge is presumed fit unless we find a source that disqualifies him. Of course, if there is a concern about falsehood, that can be grounds for local disqualification even if there is no source that disqualifies him across the board.
3. The Sanhedrin / the sages determined that the commandment of “do not deviate” applies to every ruling of the Sanhedrin. That is somewhat like the situation we are discussing.
4. You are talking about an implication that is not a personal result, but a principled implication. This is a ruling that would make someone a kohen (for example, if a judge rules that the son of a mother who is a kohen also has the status of a kohen), and what would affect me is that I too become a kohen for the same reason, because I too am the son of a mother who is a kohen—not that his becoming a kohen directly affects me. This is not a standard conflict of interest by definition, for two reasons: a. My ruling applies only to the case before me. My own case will be discussed separately, and there is no binding precedent here unless we are dealing with the Sanhedrin. b. After all, every ruling has to be reasoned, so a principled ruling of this kind will be based on arguments, and those arguments will be examined on their merits. There is no need to disqualify a person because of a conflict of interest in such a case. An example is my own arguments regarding the authority of the sages nowadays, which allows changes in Jewish law. Can I myself make use of that in order to introduce changes? Obviously yes. My arguments will be examined on their merits, and others can decide whether to adopt them or not. I now recall that this connects to the dispute between the House of Shammai and the House of Hillel, which is based on a dispute over whether the determining majority is the majority in wisdom (as the House of Shammai held, since they themselves were sharper) or the majority in numbers (as the House of Hillel held, since they were the numerical majority). There you have a case where a judge expresses a position that undergirds his own status, and nobody gives that possibility a second thought.