Is stopping tasbeeh aloud—after knowing it is obligatory—out of a dislike for people seeing it, considered abandoning an action for the sake of people?

Do not stop glorifying and remembering Allah with your heart. It is better to combine this with remembrance by the tongue, for Allah the Almighty says: "I am as My servant expects Me to be, and I am with him when he remembers Me. If he remembers Me to himself, I remember him to Myself." Moving the tongue and lips is only obligatory for devotional supplications like Al-Fatiha and the opening Takbeer (Takbirat al-Ihram). Your cessation of remembrance out of fear of people seeing you is a clear mistake. So, remember Allah with your heart and tongue, seek refuge in Him from hypocrisy and Satan, and do not abandon righteous deeds out of fear that people might see you.