"Protestants don't believe in transubstantiation which is why we don't take Communion in Catholic churches. "
The precise reason you dont take Communion in a Catholic church is that you need to go through Catholic baptism and first Communion. Whatever your beliefs, you do not partake without initiation. We believe in one catholic and apostolic church, as the Nicene creed has it.
The idea that it is 'rude' to invite someone to your own church is a bizarre one to me. One can always decline such invitations.
It's rude to invite them with the purpose of taking them from their current church because you feel your church is the only one. That's kinda considered "cultish" in Christian churches.
The Catholics may feel they are the only Christians but they don't ride herd on the Protestants about it.
Note: The Methodist Church I attend has a Book of Mormon in the library. Go figure.