Religious ceremony in Poland and Civil ceremony In Ireland?

You want to do your research carefully, esp. at the Polish end. In Poland Catholic church wedding are recognised by law, which means that as a matter of Polish law if you have a Catholic church wedding you are married both from a religious point of view and as a matter of Polish civil/state law. And the Irish legal position is that if a foreign ceremony is legally recognised in the place where it is celebrated, then it is legally recognised in Ireland too. So, if you have a church wedding in Poland and then rock up to the registry office in Ireland asking them to marry you, there's a risk they may say "No. You are already married."

There's two possible ways to avoid this risk.

One is to explore whether it's possible to celebrate a church wedding in Poland in such a way that it doesn't attract civil recognition e.g. by not filling out the civil paperwork, getting a civil marriage licence, that kind of thing. It may be that, as a matter of Polish law, there is nothing you can do to avoid civil recognition. Or it may be that, as a matter of law, there is, but the church won't co-operate. (Churches generally don't like to celebrate marriages where the couple are deliberately evading civil recognition.) So you're going to have to do your research to find out what is practical or possible in this regard in Poland.

The other is simpler; have your civil wedding in Ireland first, so that you are already legally married by the time you present yourselves at the Polish church. The church will have no problem in principle celebrating a wedding to give religious validation to an existing civil marriage. There'll be paperwork issues and, again, you'll need to do your research to find out what, exactly, the Polish church will need to see in order to be willing to marry you, and there might have to be some lapse of time between the two ceremonies while you line up the paperwork, any necessary translations, etc. But it should be possible.