How does someone who is not religious identify “scientism” and discern when they have crossed the line into scientism?
The idea that science is the only valid way in which truth may be “learned and discerned” is scientism. There are other ways – for example social sciences where you cannot perform experimental evidence per se. A lot of what else is done in social sciences is not really science.
The idea that science is capable of, or will (eventually) discover some kind of ultimate objective truth, is scientism (we don't know).
The assumption that science is capable of proving or disproving the existence of a “God” is scientism.
Here is an excellent lecture (series) on Scientism, it's dangers, and identifying the rise of Scientism in one's own mindset: https://www.youtube.com/watch?v=XFVARio4pAk