What is the ruling on one who prays the Sunnah of "greeting the mosque" out of embarrassment from people, and abandons the sin of looking at women in front of people; and is that considered major polytheism (shirk akbar) in both cases?

Performing an act of obedience out of fear of people's censure for abandoning it is considered hypocrisy (riya') and minor shirk, which contradicts sincerity (ikhlas). Sincerity means singling out Allah Almighty in one's intention for obedience, desiring thereby to draw closer to Allah alone, without any other purpose such as showing off to creatures or seeking their praise. Similarly, abandoning a sin for other than Allah is also considered hypocrisy.