Is this a thrust button and can it be removed?

It's just a matter of design. Tapered roller bearing are a superior design over ball bearings. Just about every vehicle manufacturer went to tapered in the 1950's for front wheel bearings for that reason. They handle side loads better and last longer. Are green real axle bearings bad? No, just not as long lasting as tapered roller bearings. Their advantage is that you don't need to set the axle shaft end play or pack them with grease. For most of our cars that don't see and never will see many miles put on them, they're just fine. For a daily driver, slalom car, off road 4 X 4, etc, I would use the tapered ones for strength and longevity. As far as your button spacer issue, I'd just test fit them. If they will install without bottoming out and the bearing retainer will bolt down flat against the backing plate, you're good. Just make sure you install both axles to do the test. What I would do is install one axle all the way in but not bolted down. Then install the other and push it all the way in. If the first axle doesn't move, bolt them down. If it starts to pop out, that spacer will need to be removed.
Very well put. Thanks for the informative response.