Nick Baker, a district master of the Orange Order in Devon, is to contest Torridge and West Devon for the far right party.
The Grand Orange Lodge of Ireland has refused to comment on the issue.
However, Alliance MLA Anna Lo said: "I really think they should distance themselves from Nick Baker."
Describing the BNP as a "xenophobic, bigoted party", Ms Lo added "the Orange Order here should not want to have anything to do with his standing in this party".
"I certainly believe that they need to make it very clear that they have nothing to do with him and they don't support his views, they don't support him standing for the BNP for the next general election and the Orange Order here do not support racism," she said.
The order has said the issue was a matter for the Grand Lodge of England.
Its grand master, Ron Bather, told the Irish News newspaper: "As an institution we try not to interfere with the political views of any of our members.
"We're not a far-right organisation. We have members from all over the world but ore members are entitled to stand for whatever political organisation they so wish.
"It doesn't mean that the institution supports those views in any way."
On its website, the BNP describes Mr Baker as "a family man who is deeply concerned over the implications of economic decline and growing national debt which will burden generations yet to come.
"He is opposed to Britain's participation in the Afghanistan conflict and will campaign for the immediate withdrawal of our forces from that country."
