Is photographing oneself with the Statue of Liberty and posting the pictures on public sites considered an invitation to disbelief (kufr) and its propagation, even if they do not believe in the Greek gods? What is the most extreme description of this act, and is the doer sinful or does he commit an act of disbelief (kufr)?

The Statue of Liberty does not symbolize what the questioner mentioned, nor has it ever been stated to symbolize it. Posing next to the Statue of Liberty is not an act of disbelief that expels one from the fold of Islam, nor is it considered an invitation to disbelief. However, it is surrounded by religious caveats such as violating the prohibition of statues, the impermissibility of photography for remembrance, imitating disbelievers, and the presence of mixing and the viewing of 'awrah (private parts) in this place.

Therefore, a Muslim must fear Allah and keep away from places of temptation and imitation of disbelievers.