What's the minimum distance between two iron golem farms?

There is a good write up on Village mechanics on the Minecraft Wiki. For two villages to be safely treated as separate villages, they need to be greater than radius + 32 blocks away from each other.

Not that the radius is defined as:

• The distance from the center point to the furthest door, -OR-
• 32 blocks

whichever is greater. This means that the radius is always at least 32, no matter what, but it can be more than that if there are any houses further than 32 blocks from the center

So, if your Iron Golem farms are 20x20, and the center of the village is slap bang in the middle of that, then your radius is a further 10 blocks from one side of the farm, (i.e. 30 blocks). However, 30 < 32, so we take radius=32

radius + 32 = (32) + 32 = 64 blocks.

If you are working a lot with villages/golem farms, you might find this mod handy: Village Info Mod. It will help calculate how far you are from the village center, and other useful info.

The centers are 63.639 blocks apart (from vector [0, 0, 0] to vector [45, 0, 45] as [x, y, z]) and they are read as two separate village.