Are they really only taking this stand because Amazon is looking to get a government contract for its Rekognition software, and Microsoft is trying to deter that?
I don't think it's SPECIFICALLY the rekognition contract, but that is the broad stroke. Microsoft has a strong ethics review process for all things AI, and routinely turns down fat projects because they don't pass ethical muster. The contracts that rekognition is designed to bid for, are largely in the grey zone where MS would turn a lot of things down. Government regulation would help lower the cost of Microsoft's ethics policy.
I didn't find anything on Microsoft turning down projects due to ethical issues.
However, I found a podcast with Fernando Diaz talking about the ethical problems of using AI and experimenting with users without their knowledge, which is commendable.