Mr Hogan, who is TD for the Carlow/Kilkenny constituency, was due to make an open-air speech, but instead retreated to the cathedral yesterday evening as the group of up to 150 demonstrators heckled and shouted abuse.
During his speech in the church, the minister made reference to the demonstrators, saying "its great to see so many people can't get in".
Afterwards the protesters hurled abuse at Mr Hogan as he was being driven away following his official engagement.
One man who was part of the demonstration said: "We came up here from Wexford. We will go anywhere. I'm not paying, I'll go to jail for this."
In his address the minister said he respected people's right to protest but people should also respect that in a democratic society "I have a right to speak as well".
"We are in a deep difficult situation as a country. We don't shout about it, we do something about it."
Mr Hogan said he understood "better than anybody" that people were under pressure but pointed out that the Government was "asking people to make a modest contribution" so that taxes would not have to be increased in future budgets.
One local man was escorted out of the cathedral by gardai when be began to heckle the minister's speech.
The Local Government Management Agency estimates that about 890,200 people have registered for the household charge.
This figure includes an estimated 241,400 registration forms still to be counted in postal bags in local authority offices and properties that have registered for waivers.