The big difference between outsourcing and robots is that the former is happening and the latter isn't. Productivity growth (a.k.a. robots) has been very slow in recent years. It has averaged less than 1.0 percent over the last seven years and has sometimes been negative.
By contrast, many firms are looking to outsource jobs, both domestically and internationally, on an ongoing basis. For this reason, when the NYT told readers in a story on the jobs report and the economy:
"Perhaps even more than outsourcing, the real threat to job growth for Mr. Trump’s blue-collar base comes from automation and other efforts to improve productivity on the factory floor."
It had the picture backward. At least for the immediate future, it does not seem rapid productivity growth will be a major source of job loss.