Mr Allister made the comments after the Government minister expressed regret that the Brexit referendum did not require a supermajority to pass, and suggested any vote on Irish unity should also use such a threshold.
The 2016 vote on leaving the European Union passed with a roughly 52%-48% split.
On Monday (October 23), Mr Baker told the 65th plenary of the British-Irish Parliamentary Assembly (BIPA) that the referendum “probably should have been a supermajority” of at least 60%.
Mr Baker, who was a strident supporter of withdrawing from the European Union, acknowledged the referendum would have failed under such a supermajority.
However, he said such a threshold would have removed the difficulty of politicians not accepting the result.
Mr Allister responded to those remarks and said that the "salami slicing of the Union without consent" shows "how meaningless the constitutional guarantee has become".
He added: “Whereas the musings of the wholly discredited Steve Baker - discredited by his transition from avid Brexiteer to cheerleader for imposing EU law and the Irish Sea Border on Northern Ireland - probably don’t count for much, it is worth reminding him and others that constitutional change has already happened in NI with zero consent, never mind enhanced consent.
“The constitutional position, supposedly guaranteed by the Belfast Agreement, has been radically altered by his Protocol, because, as the Supreme Court confirmed, Art 6 of the very foundation of the Union, the Acts of Union, has been suspended with no one in NI even being asked to consent.
“The Union is a political union, established by Art 3 of the Acts of Union, and an economic union of unfettered trade, established by Art 6. The economic union has been trashed with trade fettered through a customs, regulatory and partitioning border, imposed to give effect to foreign EU law."
Speaking on BBC's Good Morning Ulster, Ulster Unionist MLA Mike Nesbitt said: "There has been some confusion about what he (Mr Baker) said but let's deal with 50%+1.
"That is the law and that was agreed in 1998.
"Anything other than that would introduce an unprecedented imbalance to democracy.
"It would mean either unionist votes are worth more than nationalist votes, or it would mean that if you need 60% for constitutional change, you must have 60% for the constitutional status-quo.”
Meanwhile, a DUP spokesman said that “those agitating for a border poll are only interested in destabilising Northern Ireland”.
A statement continued: “The majority have no interest in a divisive border poll. We are focused on fixing the problems in NI and making sure our place in the UK is cemented for generations to come.”
A Sinn Féin spokesperson said: “Ultimately it will be the people of this island who will decide our future in a democratic referendum in line with the provisions and conditions that are set out within the Good Friday Agreement.”