The former first minister made the plea on the fringe of the Scottish Labour conference, while on a panel with a controversial Labour supporter of independence.
Allan Grogan, the leader of the Labour for Independence group (LFI), which is accused of being an SNP front, was jeered after advocating a Yes vote.
McLeish said: "I know nothing about LFI, but we need to be a party that is tolerant of dissident voices.
"We don't want to be known as a party that cannot brook discussion, however much it makes us uncomfortable or makes us think about things that we don't want to think about.
"And a genuine concern I have is, 'let's stop hating Salmond and the SNP'.
"I don't like the fact that Salmond won in 2007 and 2011, but let's remember somebody must have voted for him and if you look at the polls just now they are not good for the Holyrood election."
McLeish also said the union was "in decline" and needed reform, but insisted he would vote No in September. "That has never been in doubt," he added.
Also at the Law Society of Scotland debate, shadow Scottish secretary Margaret Curran said she was "delighted" that McLeish would vote No, and said he was proof that Labour that was a pluralist party.
However, she also accused Grogan of peddling "two great deceits" - that a No vote meant the status quo and that equality was impossible in the UK but automatic under independence.