Some Jewish young adults (usually, college age) think that it is 'cool' to have their bodies tattooed. Will these kids be barred from most Jewish cemeteries upon their death many years from now?

There are two primary reasons that tattoos are not accepted in the Jewish community. 

1. In Jewish tradition, and following Halachah (Jewish law), tattooing is explicitly forbidden because a tattoo is produced by the process of repeatedly inserting a needle into the skin and injecting a dye or ink. Because of the process used, it fails the test set by the Torah that one may not make a ‘gash’ or ‘incision’ or ‘cutting’ in the skin/body to mark or adorn it.
2. Some feel that in the aftermath of the Shoah (Holocaust), when so many were tattooed against their will and unwillingly as a way to humiliate and dehumanize them, to seek a tattoo as a decoration is to minimize their suffering and abuse. I am saddened to say that as time has passed, and the number of survivors has dwindled, this second reason has been of diminishing impact among younger Jews.

The overall Reform position on this seems to be in line with much of what is said in other matters: Jewish tradition is not in favor of this act, and we discourage it, but each person may act with autonomy and make their own decision about it.  

As for the concern you express about future burial, I am sorry to shoot down a myth upon which many Jewish parents have relied for years, but I don’t wish to perpetuate a falsehood.  Having a tattoo is not in and of itself enough to prevent someone who is Jewish from having a Jewish funeral or being buried in a Jewish cemetery. For example, I cannot imagine any Jewish cemetery that would refuse burial for a Holocaust survivor simply because they had a tattoo.

Restrictions on burial in a cemetery tend to be set by the rules of the cemetery in question. A cemetery run by an Orthodox group may have different rules than one run by a Reform group, and both may differ from a cemetery run by a Conservative group, but equally true is that two Reform cemeteries may have very different rules. There is no overall rule that one can refer to as the definitive statement.

As a general matter, I would suggest that the family of a Jewish person who is to be buried will be able to find a Jewish cemetery where that person can be buried. They may find that one or another cemetery will not agree, but in the end, a Jewish person is likely to be accepted for burial in a Jewish cemetery. The existence of a tattoo (or several) may affect which cemetery, but should not prevent a Jewish funeral and burial.