Hinduism has both Agamic & Non-Agamic temples
In the Non-Agamic, especially folk temples, the priests are almost always Non-Brahmans and very often from so-called Lower Castes. The priests of Aiyanar temples of Tamil Nadu are mostly Dalits.
It is a widespread misconception that the so-called lower castes cannot become priests. In India, a significant % of temples are rural folk temples. And the priests of folk temples have been Non-Brahmans. In fact, having Brahmans as priests in folk temples is a recent phenomenon.
This is a Murti of Tamil Hindu folk deity named Madurai Veeran. He was a Dalit warrior. He protected Madurai & Meenakshi Amman temples. He is worshipped as a deity by people across all castes in Tamil Hindu temples. Of course, atrocity literature peddlers won't tell you this.
The famous Tula Bhavani temple is devoted to Tula Bhavani, the family goddess of Shivaji Maharaj. The priests of the Tula Bhavani temple are not brahmins. Traditionally, the priests hail from the Maratha Bhope community.