This is Malaysia, all manner of bizarre policy exists.
But ATMs usually use payment networks (like cirrus, plus, etc.). Most global ATM machines should have a whole bunch of stickers on them listing the different payment networks it is setup to use. If yours is listed, it should work. There are some ATMs that service Malay savings, hajj contributions, etc. which may only allow their customers' use of their ATM and not be connected to other networks (ex. Tabung Haji, BSN).
I'm also not aware of any bank a non-muslim is not allowed in.
Additionally, there are a large amount of foreign banks that operate locally (Bank of America, Scotia Bank, HSBC) which have branches, ATMs and card services.
Is there fraud at ATMs? Yes, but look for odd devices attached to the card reader area (usually transparent shrouds, lit with LED lighting, are added by the bank to prevent the possibility of malicious card readers from being added), be wary of any POS payment terminal that is firmly attached (it is likely firmly attached to accommodate a camera or individual watching for your pin) and keep your pin hidden (most ATMs also have a plastic shroud to prevent people from seeing your pin). The local perception is that you are much more likely to have your wallet or purse stolen by "snatch thieves" (attacks from a team of two on a motorbike / kapchai / scooter).
Maybe phone your bank to see if they allow withdrawals. Beyond that it is unlikely (although not impossible) that all banks are preventing ATM withdrawals. Stick to major bank ATMs (Maybank, Heong Leong, Public Bank, Bank Rakyat, that bank whose mascot is an octopus, etc.) not third party ATMs and avoid Tabung Haji and BSN machines (they are kinda not banks). Otherwise head to the Bank of America branch in downtown KL.