To high self-monitors, low self-monitors seem rigid and socially awkward, but LSM would argue that they are always true to themselves and their feelings. To low self-monitors, high self-monitors can come across as conformist and deceptive -- "more pragmatic than principled," but in some cases, one might argue that high self monitoring is an act of modesty. It's about accommodating oneself to situational norms, rather than "grinding down everything to one's own needs and concerns." A more introverted version of HSM may be less concerned with spotlight seeking and more with the avoidance of social faux pas.
I am a HSM introvert.