Will bitcoin exist with the current financial system? Or will it become a parallel system that coexists like two countries exist side by side? I believe it will be a parallel system?
If you are talking about a
normal country, then yes, Bitcoin will co-exist with the fiat national system side by side. Official cryptocurrency exchanges will serve as financial gateways. Citizens investing in Bitcoin will pay taxes levied by the government and fund the budget of the country they live in.
If you are talking about a country which has
banned Bitcoin in its jurisdiction, then no. Local BTC holders will be forced to hide themselves in order
not to be punished by law enforcement officers. Bitcoin will only try to survive there. In any case, the fight against blockchain technology based on a decentralized network is very difficult, so eventually this government is likely to fail.
Even if bitcoin is banned in a country there are circumstances in which it could still be used alongside the official currency, for example if the country was going through a very important and almost permanent economic crisis then people will make the decision to still use bitcoin despite the penalties because that is the only way they have to keep their wealth.
And in the case there is a high corruption in such country, just as it is the case in most countries going through such a huge crisis, then those that use bitcoin could always get away with it thanks to that corruption.