I have the same problem on my iMac (Intel 21.5"). Most likely it is a problem with your computer's SD card reader.
Shine a strong light into your computer's SD card reader: you will be able to see a tiny, brass-coloured latch on the narrow floor of the slot. If your computer has the same problem as mine, then that latch will be sitting in the 'down' position (ie inserting the SD card does nothing to change its position).
Normally the latch sits in the 'up' position and is depressed when an SD card is inserted. With an unlocked SD card, there is a minuscule space for the latch to pop back into the 'up' position. With a locked SD card, the slider on the card blocks that minuscule space, thus telling the computer that the SD card is in locked position.
It seems to be a common problem (judging by the number of internet posts describing exactly your problem) with the Mac built-in card reader that that latch, after some usage, when depressed eventually fails to return to the 'up' position and remains instead sitting in the 'down' position, thus telling the computer every SD card you insert is locked, regardless of whether the card itself is locked or unlocked.
Why am i making this guess? Because i (and you) have tried the same SD card on an external reader and, in that case, the computer reads the card as (correctly) unlocked. The Mac card reader perpetually reads it as locked.
Solution? Apple may replace your card reader if your computer is still under warranty. Les-inconvenient solution: use an external card reader.
This just happened to me in my brand new macbook pro 2012. My Sandisk SDHC Extreme Pro card can be read but I can't delete files.
Has any one had this happened to? please help. I have searched online and very little threads on this topic, some people had this issue and even after reformatting card persisted.
In any windows computer this is not an issue with the same exact card. It is not the lock tab on the side this is not locked the info shows FAT32 read only. Why should this be a problem I thought that MAC was ok with FAT 32 cards. Frustrated.