This says the collection of names is for their religion. https://www.pbs.org/mormons/etc/genealogy.html
Shalom, Thank you for your follow-up correspondence. I have been in touch with the site “family search”, which is run by the Mormon church. As far as I can tell, the Mormon church believes in offering the souls of those who are dead, the opportunity to accept the teachings of their church, and become baptized after death. In order to do this the church collects information about those dead, which can be used in the ceremony and process of this religious practice. The names put into the site do not automatically become used in such a religious service. Mormon's who want to preform this ceremony for dead relatives can use the site as a way to determine if the dead relative has already been “baptized”, and attain the needed information in order to do the baptism. After finding a name on the site (or entering in a name and it's genealogical information), one may click on a request to start the baptism process. After clicking on such a button, an information box comes up which explains the Mormon church's policy of for who such a religious ceremony may be preformed for - only relatives, people dead for a certain time already, not celebrities, and most importantly for us, not people who were Jewish. Unfortunately, whether these instructions are followed or not is dependent on the user (and there have been some unfortunate misuses, when in particular holocaust victims names where sent for this “baptism”). Only after seeing this message can the user continue on to the request to start the religious service. Based on this information, it seems to me that using the site can be divided into three parts. Firstly, merely searching the database for information should be permitted. Secondly, putting new information into the system may not be totally forbidden, but in an effort to distance oneself from any connection with involvement with other religion's services (which stand at odds to the beliefs of Judaism) it is advisable to refrain. It may be that someone else will submit the name you have entered for the “baptism” options – against your will, and even against the instructions of the Mormon church itself – which at the very least would be unsettling to a Jewish person. Thirdly, taking part in any way with the religious service, or submitting names for such a service, is totally forbidden according to Jewish law. I hope that this will be of help. This is based on my current understanding of how the Mormon church uses it's site – but if I have understood it incorrectly, or the practices change, of course I would have to revise my answer. Blessings.