Yes, you have read this correctly. In 2019, a teacher can legally be fired due to their religious values. Despite an attempt to remove this right in recent years, it was voted down by the then Fine Gael/Labour government.
Whether or not this right has been exercised, is not the point. The fact remains that if I work in any denominational school and for whatever reason I cannot uphold the ethos of the school, I can be fired. An example of this would be an Orthodox Jew working in a Catholic school and being forced to teach the fact that Jesus was the Messiah. This is completely against Jewish doctrine and therefore this Jewish teacher would not be able to do it. However, it is legally possible for the school to fire him/her. More subtly, of course, this being Ireland, the likelihood is that this teacher would be bypassed for promotions or given a non-mainstream class.
While this is further evidence that denominational school systems don’t work, given that it is, we have to protect its employees from being at risk like this. However, maybe it’s better to have this in situ to highlight the bigger picture. As someone who is that soldier, I wouldn’t have minded definite protection while the bigger fight is being fought.