Farmers have said it is impossible to see how the Irish border can stay open and free of checkpoints under the Brexit proposals.
While the Ulster Farmers' Union (UFU) warned thousands of jobs are at risk in the North, the Irish Farmers' Association (IFA) said the UK Government will have to make more compromises on its ambitious international trade targets.
Some 40% of the exports in Ireland are destined for a UK market.
In Northern Ireland, more than 50% of agri-food produce goes to the Republic, and it is valued at more than €750m (£683 million).
As London published its border and customs proposals for Brexit, the IFA said it was difficult to see how goods and people could continue to move freely north and south if the UK operates an independent customs and trade policy separate to the European Union.
"Cross border trade in agricultural produce encompasses crucial issues such as food safety and animal health. If the UK insists on pursuing its own free trade agreements, two divergent regimes would have to operate on the island and it is impossible to see how border checks could be avoided," the association's president Joe Healy said.
"The UK will have to compromise on their future trade ambitions with third countries in the area of agricultural and food products."
The IFA said the idea of the UK leaving the European customs' union was a "hard Brexit".
And Mr Healy said a "streamlined border" option is unacceptable for farmers as it would grant the UK the right to make their own rules on imports.
"Any increase in low-cost food imports into the UK that would undermine the value of the UK market would have a devastating effect on the Irish agri-food sector. The potential displacement of Irish food exports from the UK market will in turn destabilise the EU market balance," he said.
The IFA called for a balanced Free Trade Agreement with the UK with no tariffs on agricultural products and food; equal standards on food safety, animal health, welfare and the environment; and a Common External Tariff for agricultural and food imports to both the EU and UK.
UFU president Barclay Bell cautioned that the UK proposals may not be accepted by Brussels.
"Early reaction from Europe has suggested that this will not be acceptable to other EU member states," he said.
"The Government proposal for a transitional period to help manage any change is something that we have been pressing for but they have also committed to leaving the customs union which is the basis for countries outside accessing the EU market and then negotiating something very similar going forward and we cannot take it for granted that others will agree."