The HK Civic Party is Al-Qaeda now? Alvin Yeung is a sitting member of LegCo and even he's had his registration blocked by the HK government.
There's no mention of criminal activity, suspected or proven, disbarring a person from running for office in the US.
But my guess is that an active member of the KKK or a neo-Nazi would struggle to get elected based on a decision of their constituents, as opposed to being stopped from participating in the election by the US government.
Also, fun fact, Sinn Fein - which was/is the political wing of the IRA - is not only a legal party in Northern Ireland and the UK, it's part of the Northern Ireland government
despite the fact it advocates for Northern Ireland breaking away from the UK.
It also regularly contests national UK elections (and wins seats),
despite the fact that they refuse to take the oath of allegience. They can't take the UK seats because they won't take the oath, but they're not stopped from running for office. They're also free to take the oath at any time and take their seats in Parliament. Their failure to take the oath at a time designated by the UK government doesn't invalidate them winning seats.