I live in Germany where it is customary for men to shake hands with women. Is it a sin?

This is one of the controversial issues in Islamic jurisprudence. The majority of scholars maintain that shaking hands between the sexes is unlawful except for the Hanafis and Hanbalis who permit shaking hands with elderly women who do not arouse desire.
Scholars who maintain impermissibility base their opinion on:
-The words of 'Aisha (may God be pleased with her) who said: "The Prophet's hands never touched those of a woman" (Muslim and Bukhari).
- Mu'qal Ibn Yasar (may God be pleased with him) narrated that the Prophet (peace and blessings be upon him) said: "It is better that you be struck on your head with an iron needle than to touch a woman you are not allowed to" (reported by al-Ruyani in his Musnad and by al-Tabarani in al-Mu'jam al-Kabeer).
- They maintain that the prohibition of shaking hands with a non-mahram woman is even greater than looking at her. Since the prohibition of looking at a non-mahram woman is known, the prohibition of shaking hands with her takes precedence over the former.

Some scholars maintain the permissibility of shaking hands with a non-mahram woman. They base their opinion on the following:
- The incidence of 'Umar Ibn al-Khattab shaking hands with women when the Prophet (peace and blessings be upon him) refused to do so when they came to pledge their allegiance to him.
- The incidence of Abu Bakr shaking hands with an old woman during his caliphate.
- Al-Bukhari’s report mentioning that the Prophet (peace and blessings be upon him) used to allow Umm Haram to comb his hair.
- Al-Bukhari’s report mentioning that a woman from among the Ash'arites combed Abu Musa al-Ash'ari's hair while he was in a state of ihram.

The ruling
This is an issue over which there is a scholarly debate. It is established in Islamic law that objection is not for issues where there is a difference of opinion but is reserved for omitting what is agreed upon to be a requirement. It is permissible for a Muslim to follow the opinion of the scholars who permit shaking hands with women who do not arouse desire. This is specially preferred in non-Muslim countries to demonstrate the true image of Islam and avoid embarrassing others. The scholars of the four schools of jurisprudence have permitted Muslims to follow the opinion of those who facilitate matters based on necessity and they do not consider this to contradict the rulings followed by a certain school of jurisprudence.
And God Almighty knows best.