Able2Know is a place where you can express your self without being constantly watched. This legislation would mean that Able2know could be targeted as a piracy facilitator if they don't start censoring us. This would mean that Able2know could be effectively shut down (i.e. removed from search engines and cut off from advertising revenue).
Due process for an individual isn't the issue. The charges and the resulting penalties would be against the site (in this case Able2know) for not doing a good enough job policing its members.
For example there could be a complaint about the number of Leonard Cohen songs posted here. Under SOPA, if whatever legal panel decides that there are too many Leonard Cohen songs being posted (against copyright) the government would shut down the entire site.
(not just the alleged copyright violation).
This means that sites like Able2Know would have the burden (under a risk of great harm to themselves and their members) of policing every post. The self-censorship will be done by sites motivated by self-preservation. This will cost time and money as Able2know would likely hire people for the express purpose of censorship. And since the issues surrounding copyright issues (i.e. fair use) are sometimes fuzzy and the stakes are so high, you can bet that censors will err on the safe side meaning that content that should be permitted will be removed.
The self-censorship by website owners that will be forced by self-preservation is the most insidious part of this bill. Since the censorship is technically being done by the private website owners, the issue of due process doesn't come into play.