The cross on Link's shield sprite has been replaced with a more generic symbol in some of the re-releases of Zelda 1. Take a look at the 8-bit Sword in Hyrule Warriors for an example. (Which is odd because the sprite on the adventure mode map has the cross shield.)

Interesting note: Christianity was going to be the official religion of Hyrule for a short time, hence the cross on Link's shield and the gravestones. The "magic book" was also referred to as a bible at one point.