Generally, Irish nationalist politicians have been in favour of the checks, although most, if not all, would prefer an all-Ireland response. Without this, though, there seems to be a general acceptance that given the current nature of the separate jurisdictions on the island of Ireland with different COVID suppression policies, a certain amount of cross-border policing can be justified.
It's important to note that although there were certainly some checks at the border, as the article in the question shows, this came about as part of the Irish government's rules against travelling further than 5km without an essential reason - similar checks were in place right across the Republic.
Independent.ie carried a fairly comprehensive round-up of the reactions of TDs from most parties at the time of the implementation of the checks - I've picked out those from the Fianna Fáil and Sinn Féin parties below. Generally, they are in favour - on the understanding that these checks are implemented across the Republic and not to the border specifically. Indeed, the suggestion that checks would be applied specifically on the border are described as an attempt to distract from the government's "failure ... to pursue an all-Ireland strategy".
Fianna Fáil TD for Sligo-Leitrim, Marc MacSharry, called for the
Border to be “manned”, even though he admitted that he hates “the idea
of a border post”.
“Let’s man border posts, but allow the hundreds and thousands of
people who have to cross it every day for work, education, family care
or essential shopping [to do so].
“They would get to know people who live along the Border very quickly,
and are back and over 20 times a day for essential purposes.”
...
Sinn Féin TD Pauline Tully, in Cavan-Monaghan, said that it should not
make a difference where in Ireland you are – if you are more than 5km
from your home; you should be fined.
“It should be strictly applied to the Border between the six counties
and the 26, it should be applied all over the island in equal
fashion,” she said.
Sinn Féin TD Pádraig Mac Lochlainn also said that an all-island
approach is necessary.
“This measure reinforces the all-island public health message that
non-essential travel should not be happening,” he said.
His party colleague in Louth, Imelda Munster, said that people in
border areas cross over and back several times a day.
“The realities of life in border areas must also be recognised, where
people need to cross the Border on a daily basis for essential
reasons.”
“Cross-border fines show the need for an all-Ireland response,” said
Ruairí Ó Murchú, Sinn Féin TD in Louth.
He also said that the Government needs to engage more with the North
and the UK government to “deliver an all-Ireland or two-island
response to combat the pandemic”.
Cavan–Monaghan Fianna Fáil TD Niamh Smyth said that there is “no
doubt” that people have been flouting restrictions by travelling
across the two jurisdictions.
“We have two jurisdictions, that’s just the makeup of our island at
the moment, and we have to have a targeted approach to make sure that
the numbers are pushed down.”
Cavan-Monaghan Sinn Féin TD, Matt Carthy, said that the Border checks
may be used as a “distraction” from the Government’s “failure” to
address issues around international travel.
“I do fear that there is an attempt by Government to use checks in the
Border region as a distraction against their failure to adequately
address international travel or to pursue an all-Ireland strategy to
tackle Covid-19.”
When actual North-South border restrictions were suggested in the Oireachtas in deliberations on the Health (Amendment) Bill 2021 at the beginning of March, to complement the travel restrictions proposed on international travel, this was swiftly challenged by Sinn Féin Senator Niall Ó Donnghaile;
Senator Gerard P. Craughwell
[...]
I cannot understand why we have not and are not considering putting checkpoints on the Border. If we restrict travel into the country through Dublin, Cork and the various ports, we must also ensure that the same restrictions apply on the Border if the exact same systems are not in place in the North of Ireland. [...]
Senator Niall Ó Donnghaile
[...]
I will conclude by responding to Senator Craughwell’s point about the Border. I do not know what the Senator’s obsession is with having boots on the Border, considering that the whole momentum of this State and of political life here has been that one could not and should not be trying to police the Border. A comprehensive fortress Ireland should be in place. If we can do that for animal health, for cattle, it should be in place for people. It is not too late to take that approach.