Airport

The airports are open. A lot of flights from affected areas have been cancelled but this was an operational decision by the airlines, it was not dictated by the Irish authorities. Here is a link to Dublin Airport's current info. on the virus....

https://www.dublinairport.com/latest-news/2020/02/27/covid-19-update

As it says, there are information desks in the baggage halls, they're right at the point where you exit through customs to the arrivals area so you can't miss them. They will not stop you, it's not a police checkpoint, they are civilian employees of the Irish health service. You can ask them for information or just ignore them.

If you will be staying by yourself in (e.g.) a hotel, it would be advisable to ask them what you should do if you find yourself showing some symptoms of the virus. The procedure is that you do not go to a hospital or a doctor's surgery, you phone the health service and they will tell you the next steps. The people in the airport will give you all you need to know.