school got involved with a twitter account?

[jpturboprop]

I would agree with most of what you say. It does seem to be an invasion of privacy. On the other hand, this is a problem that goes far beyond individual rights. It is about expectations, as well. You and I expect to be able to access any site on the internet as long as the site is posted. It is not the school's role to determine what web content is on line at any point in time, other than specific content that they post, and content they feel is libelous. In the case of libelous material, the school has the right to ask a court to remove the material, but cannot do it themselves.
As to notifying your parents, that is anyone's guess as to their legal status to do that. Considering that the schools seldom contact parents when a kid is sick at school (just go down to the nurses office...) it seems a bit over the top that they should be concerned just because you are following someone on Twitter...