Bird's nest fern are not parasitic but they are epiphytes, meaning that they don't grow in the ground but on trees. I'm not sure what the other is but I think it is also some kind of epiphytic fern. So the trees probably aren't being harmed. Beautiful specimens!
Thank you @nikv for taking a look, and for your input. I learned something new today.
I used to think that Bird Nest Ferns don't grow on the ground too. But recently, I came across these.
So, maybe the Bird Nest Ferns grew both on and above ground.