Mr Parker made the comments in an interview with the Herald as part of a series on the four leadership contenders.
He said part of the overhaul as Labour tried to recover from its damaging election loss should include its branding, which was the shopfront of the party most noticeable to the public.
"At the moment I think we present ourselves in the Labour Party as so ... well, some of our imagery is so clearly 'Labour red'.
"The image we have of ourselves is sometimes really nice, like at the campaign launch.
"But on other occasions it almost feels like a cult. And it becomes a barrier to entry."
He stopped short of saying Labour should ditch the colour red.
"I don't want to over-emphasise that, it's not the main point. But we have to be more accessible and make people comfortable with us."
Mr Parker recalled former National MP Katherine Rich being criticised for wearing a red dress because it was a Labour colour "and she'd say, 'It's a political party, not a cult'."
During Labour's election campaign, former leader David Cunliffe was also criticised for frequently wearing his red scarf.
He responded by saying he would not wear it as much, but added: "You know what? I reserve the right to put it back on occasionally ... I quite like the colour red."
Mr Parker said the ideal solution was to build a more conversational relationship and have a party similar to a convivial dining companion, "the sort of person you'd invite round to your house for a drink or afternoon tea and feel at ease with".
He said people had to feel they could trust Labour and could be proud to associate with it.
Labour adopted red - the colour long associated with the international socialist movement - right from its beginnings in 1916, and until the late 1940s, members closed their meetings by singing the socialist anthem The Red Flag.
Party secretary Tim Barnett said aspects of Labour's branding and possible changes would be examined in its post-election review.
"I wouldn't say the colour's a live debate and the logo's reasonably new ... I haven't heard a lot of discussion about that either."
Suggestions Labour had cult-like aspects were "not language I've heard, but it doesn't mean to say it's not a point of view people have and will want to pursue".
Mr Parker and the other leadership contenders Nanaia Mahuta, Andrew Little and Grant Robertson will hold the first of 14 meetings with party members tonight in Wellington.
- By Claire Trevett of the New Zealand Herald
