Judaism views burying the dead as a supreme mitzvah. While in some societies gravediggers and undertakers are viewed with distaste, membership in the local chevra kadisha, or burial society (lit. “holy fellowship”), is a position of great distinction in any Jewish community. There are no social disabilities attached to any such function, and it is a privilege and honor to know people who are willing to engage in chesed shel emet, acts of true loving kindness.
It is true that Jewish law assigns a high degree of tum’ah, which can be imperfectly translated as “ritual impurity”, to those who come in contact with corpses. When the Temple was extant, this meant that chevra kadisha members were often unable to enter the Temple or eat certain kinds of food-taxes given to kohanim (members of the hereditary Jewish priesthood). However, this simply added to their stature, as everyone respected their willingness to surrender their own opportunities for spiritual gratification for the sake of chesed shel emet.
The major consequence of this law nowadays is that kohanim may not be members of a chevra kadisha, although they are required to incur tum’ah at the burial of their close relatives. It should be noted that the type of tum’ah incurred by contact with (or other types of association, such as being under the same roof as) corpses can only be removed by a ritual involving the ashes of a “red heifer”, which have not been available for more than a thousand years. Jewish law therefore generally presumes that all Jews nowadays have acquired this tum’ah whether or not they are professionally involved with burial.
The chevra kadisha is generally a volunteer society, however. As with any mitzvah that becomes professionalized, such as firefighting or teaching Torah, there is a risk that it will be done with indifference or corrupted by greed. One should be overjoyed to shake the hands of funeral arrangers who genuinely consider the honor of the dead, and the honor and needs of the living; one should refrain from shaking the hands of funeral arrangers who take advantage of emotional distress to create needless expenses and the like, but not because of tum’ah.
Answered by: Rabbi Aryeh Klapper