"Plastic paddy" is a term used to describe people who pretend to be Irish but aren't really Irish. Imagine you have toys that look like animals, but they're not real animals. They're pretend animals, but they still look like animals. That's what "plastic paddy" means - someone who looks like an Irish person, but they're not really Irish.
For example, someone who wears a lot of green, talks with an Irish accent when they're not Irish, and claims to be Irish but doesn't really know much about Ireland or Irish culture could be called a "plastic paddy."
It's important to remember that it's okay to appreciate different cultures and traditions, but it's not okay to pretend to be part of a culture that you're not. It's like pretending to be a doctor when you're not qualified - you might think it's fun, but it can be disrespectful to people who actually are doctors.