Nearly three quarters of the country think Leo Varadkar's sexuality will not damage his chances of becoming Taoiseach.
A new Millward Brown poll found that 72% of people believe coming out as gay will not influence the career of the health minister.
Voters were also asked how they plan to vote in the same-sex marriage referendum. The response was an emphatic Yes, with 62% claiming they will vote in favour of it, 16% saying they will vote No and almost a quarter saying they did not know which way they would vote.
The poll also found that more than half the population wants a referendum to decide if we should repeal the 8th amendment on abortion.
The poll shows how people feel about the main political parties too - showing Sinn Féin as the most popular party in the country, with gains for others at the expense of Independents.
Meanwhile, satisfaction with the Government goes up four to 23%, while the four main party leaders see their satisfaction with voters also go up.
On water charges, 40% who participated in the Sunday Independent poll said they would definitely pay the bills, while 30% say they definitely will not.