The word "radicalize" is an another media uses to refer to those whom
disagree with a policy, official pronouncements, and views promoted by
the governments, the churches, and now the SSPX.
Is to demonized the opposition no matter of their sound reasons for
disagreement. Make people whom are on the fence on a particular issue
fear to come to your side because of name calling.
The liberals playing the demonized word game can cause to much fear
in the masses, and can get their ideas, and programs through no
matter of the eventual consequences of their agendas.
The liberals will not debate issues that they want.  And will use the
word game to shove their programs through regardless of the harm
it does to society and the church.
Most of us have a brainwasher in the house, and that is the TV.
A few can determine agendas seen by millions. If you do not like it
turn the set off. However, on a very few have the courage to do so.
Because they like the ball games and the soap operas.  And this is how
the masses get locked in with the brainwashing.

As I understood it, "radicalization" was a political science term that generally referred to people who had been pushed too far and, as a result, were ripe for political mobilization.  So people like former peasants pushed into factory jobs relatively far away from their home villages or former housewives pushed/lured into the labor force or former factory workers in america or hippies who found out "free love" wasn't free, ect were often quite discontent with the state of things and often felt disconnected from things around them.  They often experienced a strong sense of alienation from their surroundings.  Hence, they were often bitter and angry, as well as lacking a desire to preserve the community around themselves, even perhaps wanting to destroy it/make some major changes to it.  So, those kind of people were much more likely than others to respond to a revolutionary/reactionary (counter-revolutionary) message.  

Most people tend to want to "conserve" the community around themselves and the way it is organized.  Hence the term, "conservative" and the reality that most people are in fact "conservative."  Iirc, they are what Nixon called "the silent majority."  

Therefore, trads should fall into the category of "reactionaries/counter-revolutionaries."  They or their parents should also have some history of radicalization.  Not surprisingly, trad chapels often seem like hotbeds of counter-revolutionary fervor and "paleo-conservativism."  Of course, that makes them targets for revolutionaries and "conservatives/neo-cons."