Can open manually

Not sure how to fix this, but our garage door opens manually and with the opener.. Obviously for security reasons we don't want the door to be opened manually.

If the door is opening via opener too, what can we check to get it working correctly, so that someone can't just lift the door to get in?

It's an older Craftsman opener from the 90s, I believe.

Not much you can do short of buying a new opener. There were a few openers made in the 80's & 90's that you could do this with. I'm not aware of any of the newer openers you can do this with. Liftmaster has the "posi-lock" built in so lifting the door doesn't bleed back into the motor allowing it to move in reverse. Most manufacturers have this.

But I feel like this is a new issue.. something that wasn't an issue the first 3+ years we've lived in this house.

Jeffrok

A Craftsman (Liftmaster) door opener should not allow the garage door to raise Manually (when connected) however, without seeing it it is hard for me to say why it would do this.
I am guessing the arm that hooks to the top section is running back on an angle (/).
If you adjust the arm (you may need to cut its length) so it is almost strait up and down when the door is closed. (you will have to adjust the open and close limits)
Then it will not be able to raised manually. If you need to raise it from the inside manually. Disconnect it with the pull cord and pull back slightly when lifting the door.