There is nothing new about people trying to get rich from religion. There are many examples in the Hebrew Bible of priests who abused their role for personal gain, the sons of Eli for example. The prophets regularly condemn priests who take bribes or other prophets who give their messages for a price (Micah 3:11, for example). The practices of indulgences in the medieval church is one of the worst examples of money extorted to generate extreme wealth for religious leaders.
In modern America, this is a real problem. There are many evangelists and media preachers who have made obscene amounts of money from their religious practices. Most educated people laugh off the conspiracy-laden evangelist who sells buckets of survival seeds so his viewers can make it through the great tribulation, but the fact is these scam artists continue to extort money from the elderly and the gullible. I would also include sub-Christian groups here as well; cults form around a central, charismatic teacher who has the real truth” (everything else is “fake news,” let the reader understand). The true follower donates all their money to the leader in order to learn the real mysteries of the universe!
Paul faces a similar problem with the opponents in Ephesus. Some of the elders and deacons in the churches are teaching things that deviate from Paul’s gospel in both doctrine and practice. It appears from this passage that at least one motivation for this deviation is personal gain. Perhaps the wealthy women who were the subject of serious correction in chapter 2 are patrons for these opponents. Patronage was a standard way for a philosopher to support himself in the Roman world, so it is not too far-fetched to think that some of the elders and deacons who have rejected Paul’s gospel have found some patronage among the wealthy in the church.
Paul is not against supporting those who teach in the church. Only a few lines prior to this passage Paul stated the elders who teach ought to be paid because they are worthy of “double honor” (1 Tim 5:17-18). The problem is the elders who are teaching unhealthy doctrine are doing so for personal gain. Just as in the modern world, it is likely that the unhealthy doctrine taught by these teachers was more popular that the Pauline gospel.
This is such a serious problem that Paul calls this a “different doctrine” which causes those who teach it to be “depraved in their minds” and “deprived of the truth” (v. 5). Paul is not dealing with a difference of opinion on serious theological or practical issues, he is dealing with a defection from the gospel which prevents people from hearing the truth.