Do people who support the restriction of free speech ever think that it is their own free speech which will...?

Yes, unfortunately, many people seem to labor under the conviction that there is one set of rules for them and another completely different set of rules for everyone else. Usually it's the same people who preach about equality for everyone and acceptance and respect for all beliefs and lifestyles, but that's only as long as those views coincide with their own. They champion over OUR rights to free speech AS LONG as what you have to say agrees with THEIR viewpoint, but if you take a different stand, then they point the finger and paint you some sort of fanatic. What can I say? People don't want to see you can't have it both ways, wanting fairness and democracy only when it's to their advantage and not when it isn't.