Is it permissible for an atheist father to reject the guardianship of a Sufi uncle if the father does not lie, given the girl's fear that her marriage contract would be invalidated if her guardian is an immoral person who does not pray?

If the girl is Muslim, it is a condition that her guardian (wali) be Muslim. If the father is an atheist, his guardianship is not valid, and the guardianship transfers to the closest male relatives in order of precedence (asabah). Justice (adalah) is not a condition for the guardian according to the most authoritative opinion. Regarding one who neglects prayer out of laziness, the majority do not consider him a disbeliever. Accordingly, if your brother is not denying the prayer, then he has the right of guardianship for marriage and is more entitled than your paternal uncle. As for the paternal uncle, generally a Muslim's affair is presumed to be sound, and his condition is not inquired into. The Sufis are not all in the same state; some of them exaggerate to the point of disbelief, some practice polytheism out of ignorance, some are innovators, and some follow them for asceticism.