After programming the chip and running “security” operation, my chip still passes blank check. Is it OK for a chip to pass blank check after programming?

Some secured chips passes blank check even after programming. This is normal.
1: 87 series chips: read data is 0x00
2: 89 series chips: read data is 0xff
3: Cypress chips: read data is random.
4: Ti and NXP chip: cannot be read

So you may ignore the fact that blank check is passing on a secured chip which has data programmed on it.