Whatever happens with Brexit, it's very unlikely there'll be a "hard border" between the UK and ROI. The UK and ROI have a common travel area agreement that predates, and does not depend on, the EU.
The ROI, like the UK, is not part of the Schengen agreement area and so is outside the "EU border" anyway. It's very difficult to imagine a scenario where Ireland would want to give up the CTA in favour of Schengen, even given the circumstances of Brexit.
Even if the UK fails to negotiate full free market access or a free trade agreement with the EU, any restrictions would almost certainly relate to services, not the free movement of goods.