Is buying bitcoin with paypal legal without laundering concerns? I'm a software developer, and I want to make a website that allows users to sell bitcoin instantly for paypal cash without the hassle of an exchange - I don't even want to make a profit from it. The idea of it is to be a 100% fair exchange, instant, and no account/signup needed to encourage more people to use bitcoin.

Regardless, I was thinking last night and wondered if money laundering here is a concern? For example, a user stole bitcoins and sold it with my exchange. Is it the sellers responsibility to ensure funds are clean (since we are dealing with fiat cash)? What if someone buys bitcoin with dirty money and tries to sell the bitcoin on my exchange for clean the money? Would the seller be in trouble even though there is know way to know funds are legit? I am in the US.
While I’m not an attorney, the website you describe would be considered a “money transmitter business” (MTB) which, in the US, falls under the jurisdiction of The Dept. Of Treasury FinCEN (Finacial Crimes Enforcement Network) which has regulations to prevent money laundering with strict anti-money laundering (AML) policies. You would need to register with FinCEN and comply with their regulations to legally perform such transactions on your website regarding AML/KYC (KYC is Know Your Customer). MTB laws also vary from state to state when it comes to cryptocurrency exchange for fiat money or vice versa. Just make sure to consult with a lawyer before you go live to protect yourself.