I have a jar that the lid is secured to the glass BUT the button still moves up and down. Is it safe or not?
The button on a metal lid- whether purchased or home canned- is an indicator of a vacuum in the bottle.
During canning, a vacuum is formed that sucks the lid on tight and pulls in the button so it can't be depressed.
If the button can be "popped" then there is no vacuum and the bottle is not sealed. If the lid doesn't move that just means it's stuck not that it is sealed.
This means that the safety of the food is compromised. If you just canned the bottle then you can either try to can it again with a new lid or put it in the fridge to consume immediately. If it has been in your pantry then consider it spoiled and throw it out.
Incidentally- having a button not pop does not guarantee that the bottle is sealed. Rarely, the button will be sucked in and the seal will fail but the button does not pop back out. If the lid is stuck in place you would discover this when opening the bottle as there would be no resistance from a vacuum. After bottling, I gently check the seals on my lids even if the button is in.
A "safety pop-up button" on a glass jar with a metal lid is 'safe' if it won't press/click when you buy it.
Once you've opened it there's no way to make it not click when pressed.
That's why it's a safety button.
If it clicks before you open it... then someone else has already opened it & it is no longer 'safe'.
If you opened it yourself, then it's 'safe' as regards interference & subject to the usual rules of how long you can keep it in the fridge, etc.
The safety pop-up button is not an indicator of freshness, it is a tamper-proof lid. Once opened/tampered, it becomes 'just a lid'.
Late note: I hadn't spotted the 'canning' tag, of which I have zero experience. I was assuming consumer store purchase.