Rabbi Yehudah said: He does not have to be a nazir, as a doubt of nezirus is resolved leniently.
The Mefaresh explains that we do not rule that he should be a nazir based upon our uncertainty, since we do not want that he should offer unconsecrated sacrifices (if he is actually not a nazir) into the Beis Hamikdosh upon conclusion of his nezirus.
It should emerge, according to this logic, that nowadays, when there are no korbanos, and the aforementioned concern is not applicable, Rabbi Yehudah should agree that we should rule stringently that he is a nazir.
However, the Maharam Mipadava (71) writes that we find many places that the ruling does not change because perhaps the Beis Hamikdosh will be built the following day. So too, here, we say that the Beis Hamikdosh might be built the following day, and he will be bringing unconsecrated offerings into the Beis Hamikdosh. Therefore, the ruling remains that he is not regarded as a nazir.