I just read that in his letter to Yemen the Rambam says that the purpose of trials in the galut is to distance people who arent truly faithful to the religion away from it. Does this mean that the Rambam says we shouldnt try to be Mekarev people who arent Tinokim Shenishbaim (like someone who grew up religious) ?

Shalom, Thank you for your question. In general we need to distinguish between reasons given for different events, and figuring out the way we should act. For example, we see that Hashem wanted to punish the Jewish people in the desert, but Moshe prayed and “argued” with G-d to save them. Even if G-d has a reason to act in a certain way, we must still strive to do what we are obligated to do. In this case, even if we explain that the bitter exiles have the Devine purpose to purify Am Yisrael, we still have a religious duty to do all we can to help our fellow Jews. Hashem will then do what is proper in His eyes. Blessings.