Disclaimer: not a historian, but am Iranian and family is Shiite. If no historians take a stab at it, I can give a bit of an explanation that might help.

I'm not entirely sure about what you mean as religious class? Iran was extremely poor for the last few centuries, and some families would send a son to be raised by the clergy, where he could get fed and given an education until he was a young teenager. After that, the teenager might come home to start working, or he might even further his education in the clergy. To understand why families would send a child to the clergy, you need to understand the context of the time. Iran was considered one of the five poorest countries in the world at the turn of the 20th century and went through a devastating famine during WW1; people couldn't afford to get their children educated, and typically needed them working from a young age. The Shia clergy acted as a charity to provide some necessities for the poor, whether it was food, education, or just general guidance. The clergy owned considerable amounts of land in Iran, but the clergymen themselves lived very humble lives due to the views on decadent living etc. They owned nothing and typically lived off the hospitality and donations of others when travelling. The clergymen were respected as highly educated and knowledgeable, in contrast to a large part of Iranian society which were illiterate farmers.

Until the Islamic Revolution of 1979 and the rise of Ayatollah Khomeini's faction, the Iranian clergy were overwhelmingly "Quietists", and wanted nothing to do with politics. The role of the clergy was viewed as staying in the Mosque. Before Khomeini, there was Sheikh Fazlollah Nuri, who at the turn of the 20th century was trying to push for more Islamic influence in Iranian politics and in the constitution reforms of 1905-1907. However, he was seen as a pariah even within the clergy and was eventually executed for treason. Sheikh Nuri's legacy was viewed as a pariah amongst the clergy until the Khomeinists revived him as a hero in the late 70's and onwards. This view of "Quietism" within the clergy relates to how Iran could have had a secular democrat vote in the 50's, while also having a very conservative and religious population.

The Iranian clergy as it is today has really only been like this since the Iranian Revolution, where Khomeini's faction skyrocketed in popularity in just a few years. It was further cemented by an 8 year war with Saddam and his Gulf and Western backers. The days of Khomeinism in the clergy is arguably reversing.