Praise be to Allah.
There is nothing wrong with a man greeting his mahrams, or with a woman greeting her mahrams, by shaking hands or by kissing. There is nothing wrong with that. The mahrams are the ones who are mentioned in the verse in which Allah, may He be glorified and exalted, says (interpretation of the meaning):
“…and not to reveal their adornment except to their husbands, their fathers, their husbands fathers, their sons, their husbands sons, their brothers or their brothers sons, or their sisters sons, or their (Muslim) women (i.e. their sisters in Islam), or the (female) slaves whom their right hands possess...”
So mahrams include maternal uncles, paternal uncles and others.
The following are the mahrams: her father, her grandfathers, her mother’s father and grandfathers on the mother’s side, her sons, the sons of her daughters and the sons of her sons. The woman’s brothers and the sons of her brothers are also her mahrams, as are her maternal uncles and paternal uncles; all of them are her mahrams. The same applies to her husband’s father, her husband’s grandfather, her husband’s son, his son’s sons and the son of her husband’s daughters; all of them are mahrams to her.
There is nothing wrong with a man kissing his mahram - his paternal aunt, his maternal aunt, his mother, his grandmother and his sister. There is nothing wrong with him kissing them, but it is preferable for him to kiss her on the head, especially if she is an adult, or on the nose or on the cheek. The majority of scholars regard it as makrooh to kiss on the mouth except the husband; it is better for that to be with the husband, not with mahrams. In the case of mahrams, kissing should be done on the head, the nose or the cheek. This is what is preferred and is appropriate.
It is all the same whether the mahrams are mahram by blood or through breastfeeding.
The mahrams through breastfeeding are the woman’s father through breastfeeding, her paternal uncle through breastfeeding, her maternal uncle through breastfeeding, her husband’s son through breastfeeding, her husband’s father through breastfeeding. They are like blood relatives because the Prophet (blessings and peace of Allah be upon him) said: “What becomes mahram (forbidden for marriage) through breastfeeding is that which becomes mahram through blood ties.” This is what he (blessings and peace of Allah be upon him) said. So blood ties are like ties through breastfeeding. The same also applies to ties through marriage (in-laws), as mentioned above. The husband’s father is a mahram by virtue of ties through marriage. The husband’s grandfather and the husband’s son are also mahrams by virtue of ties through marriage. Whether (the mahram relationship) is through ties of blood or through breastfeeding, shaking hands is more appropriate.
Shaykh ‘Abd al-‘Azeez ibn Baaz (may Allah have mercy on him).