I think you've hit on a major problem in attempting to draw a line between 'desirables' and 'undesirables'. It's rather arbitrary, and will inevitably be rather ham-fisted (as it's dealing with a large number of people and shift them into categories, it always happens).
I'd personally endorse your latter suggestion. I don't think extremism* or 'undesirable' views is on their own are grounds for being barred entry (unless you have well-established ties with terrorist groups or something - but seeing evidence for that's more an issue of global police co-operation). I don't think the fact that these peoples' presence will cause others upset necessarily warrants govt. action. With the globalised communication that we have, it's pointless to attempt to shelter ourselves from repugnant viewpoints. Best to let them stand up and be cast down again by public scrutiny.
*emphasis on 'on their own'. I'm not saying we should unconditionally allow extremists in the interest of pluralism, obviously if there's evidence they're connected to terrorist groups or fail to meet an allready-established criteria under immigration policy, they shouldn't be allowed in.