For one thing the 'shadow' effect appears in different directions on different patches.

Also, if this was intended to create a 3D effect on the lettering, why would they also do it on the earth, making it look like a flat disc?

Although I stand by what I said above about this effect being an issue with misalignment of the various stencilled elements of the design rather than a deliberate feature, I have since noticed that some patches seem to show misalignment without the noticeable 3D/shadow effect.

What I realized is that there is a distinct variant of the Apollo 11 beta cloth patch where the black outline around the lettering and the Earth was apparently removed from the stencil that includes the three concentric outer circles. Misalignment can stil occur but is much less visible without these outlines, making the resulting patches much cleaner looking.

It will certainly be possible to find perfectly aligned versions of the older variant but most patches without a shadow effect on the lettering are likely examples of the later variant.

The variant version has some other noticeable differences in the design which I've mentioned in the updated beta cloth page of my CrewPatches site. Note that the later variant is the one that appears in the Owens Corning Apollo 11 lucites and on their Apollo Missions beta cloth presentation. I've also added a brief mention of the various presentation pieces on the page.