Thanks for being easy with my serious question. Your detailed explanation really enlightened me.Your original question was a valid and serious one.
My answer is that "If we have our religion registered on the paper, we will not be able to join the party" is grammatically correct, but it leaves out some important information.
1. The phrase "on the paper" is not one we usually choose when talking about a government document - I think you would probably say "on the form" (a form = a printed document into which you write answers to questions such as: Name, address, religion, etc.) "The paper" alone usually means a newspaper or an exam paper.
2. You don't say what political party you're referring to, just "the" party. This would be unusual in the country I live in, where there are dozens of political parties, but in other countries, or if the name of the party has already been mentioned in a previous sentence, it might be OK.
You can also say "If we have our religion registered on paper... " (without "the"). This means "registered in written form / registered officially / written down / in black and white".
Thanks for your tips. You are right, I meant the Communist Party.It sounds as if you wondered whether 'on the paper' could be omitted.
I think your sentence works if you just say, 'if we have our religion registered'. No need to say where.
On reading your sentence, I assumed party = Communist Party of China. I think in the context of China, many people might make that assumption. It all depends on your audience. If it is clear that the discussion is about China, and the audience know about China, just saying 'the party' might work. When communicating with someone elsewhere, you should make it more specific.