I have been in schools that have an office in the front where people enter and someone will immediately come out and question why you are there.
I have also been in schools where you could wander aimlessly all day and never get a second look. I worked for a group home and one of our kids didn't come home on the bus, so I had to go to his high school to see if he was there. I walked up and down every hall, into gymnasiums, and around the grounds and not one person stopped me. I had to go into the office and "ahem" before anyone assisted me. I could have been a PO parent looking to abduct my son/daughter, a pedophile, or some sick person looking to plant a bomb, and nobody even cared.
No, I don't think most schools are safe at all. It's pretty scary that most post offices/court houses have better security than schools