Very many people object to being preached at.

Indeed! Good training should teach preachers not to preach at people, nor beyond people, nor above people’s heads, nor beating around the bush, but to people in a manner designed to engage their attention.

However, many people do not want even this.

So they cannot complain if they are left to their own devices. As Jesus said of some people: “Leave them alone: they are blind leaders of the blind, and if the blind lead the blind, both shall fall into the ditch” Mat 15:14.

The consequences

The consequences are explained by the apostle Paul.

“Whosoever shall call upon the name of the Lord shall be saved. How then shall they call on Him in Whom they have not believed? and how shall they believe in Him of Whom they have not heard? and how shall they hear without a preacher?”

The apostle Paul: Rom 10:13-14

So if people don’t want to hear Christian preachers, they cut themselves off from the Gospel of salvation and carry on with their native opinions of their own goodness or with another false religion. They will have to give account of themselves to God. Jesus warns them that they will not succeed, but they do not want to hear this either, nor the solution.