Yevoners aren't trying to control the world through the teachings like the old temples did.
Wakka explaining Yevoners to Chuami
Yevoners are a religious organization referenced in Final Fantasy X -Will-.
Yevoners follow the teachings of Yevon while accepting cultural differences on Spira. It's just one of many ways to live their life. Respecting your neighbors, gratitude for nature and striving for peace are the beliefs Yevoners focus on.
Even in the new age many people still felt lost. Not being able to break old habits, they gathered once again to create a following. Yevoners focus more on the teachings of Yu Yevon instead of New Yevon, which was more into politics.
Yuna has become a priestess for the religion, praying peace for Spira in Besaid Temple. Yevoners are viewed as a gathering of weak people by many, but Chuami appears to be the only one outspoken about their backwards practices. Instead of hiding, she believes the Yevoners should try to live.