The answer is yes and no. I know that internet computers used in the church have a function that does not allow to show websites other than intended for the use of the computer. Like someone whose job is to buy supplies would not be able to spend his time with reading message boards or anti-Scientology sites (or Scientology Myths). He could do this at home though and I plenty of times when I was talking with Church staff about anti-Scientology websites they knew what I was talking about. I think it is pretty common that your boss doesn’t want you to doodle around on the net when you are supposed to do your job. So that’s a yes here. 10 years ago there was a spam filter, probably the first of its kind, for people who wanted to get blocked on spam. And as any software you could install it and uninstall it. As a special function it did warn the user when he/she was about to access one of a list of certain anti-Scientology websites.
I did not much with the internet that time and have not seen this software in operation. I actually don’t know anybody who used it and it is sure not around today. There are no restrictions for Scientologists to go online and inform themselves or have blogs and so on.