We also buy office supplies from a company that's not owned by a Christian.
Hammster pretty much boiled Scripture down right there.
The hard part of the answer to the OP's question is not what God wants (unless he speaks to committee members). To follow Christ it is impossible to keep in step with a world that gets its moral code elsewhere. God commands Christians to separate themselves from bad influences, but he doesn't give us a complete list of what those things are. He also commands Christians to stay among non-Christians. Scripture provides a lot of help for deciding whether to accept or reject a particular product, service, or association, however the final decision is ultimately up to the people involved. More interestingly (perhaps) is that God doesn't even itemize the criteria by which we should make those kinds of choices. Not surprisingly, this is a matter that has a huge variety of perspectives among Christians.
Some Christians as well as those with different or no particular spiritual beliefs, approach the question from the standpoint of whether they would be helping to promote something they want promoted or something they want curtailed. (It's been called "voting with your wallet" and similar things.) However every such person must draw a line somewhere. The ones that want to promote as little as possible head off to live off the land. Other people recognize God loves everyone and are happy to help put food on the table of any human. God does not draw a clear line for the general Christian population.
However, this is all predicated on the fact that the hypothetical question does not provide any information about how using the service would promote (or not) the "cult" or what that "cult" teaches or does. (As such, it probably is the most common context that people must deal with.)
That Christians express distaste for certain other people (people in a "cult" in this thread) is most commonly the result of either the subculture they grew up in (which forms their conscience) or harm they have received from others. Both can produce a pain avoidance mechanism that we see as self-righteousness—which seeks to make oneself feel better about themselves. No one, Christian or non-Christian, is immune to this. Self-righteousness as well as the things that bring it about are not from God. To be more like God is to be more gentle and humble (Luke 22:25-26). Distaste for people in a "cult" can come about for several reasons (probably more than I point out):
1. They have both an unchanging moral standard (revealed through Scripture), and various subcultures which nurture using it as a tool of self-righteousness. Their mistake is in how they handle the idea that they know how another person should be living their life. No one knows how a stranger "should" be living their life. God doesn't expect anyone to become an instant saint upon choosing to follow Jesus. He works on a limited number of aspects of a person at a time. About the only thing a Christian knows about a non-Christian stranger is that they need to know about Jesus' sacrifice to pay for all their sins against God and that they are now forgiven. The way God handles non-Christians is to love them and to speak/convey the truth. It's up to the listener what they want to do with it. That's how God teaches his followers to handle it, too. It's up to the Christian to be an example of someone that believes in and trusts Jesus Christ, who is alive and well and will help them, otherwise their testimony is going to come across as not credible and
make things worse regarding how people receive what Christians say. The bare-bones core of Christianity has nothing to do with behavior, anyway.
2. Too many Christians have chosen not to give all of their heart and life over to God's Lordship so that he can do what he wants with them. That makes it impossible to handle the previously mentioned matter well. We are commanded to make Jesus the center of our lives—be the number 1 thing on our minds and actions. There is huge reward in this life and the life to come for doing this. To the degree we don't do this is the degree to which we end up having chosen to to follow the ways of the world. This is often just summarized with a statement that conveys a sentiment like "too many people that call themselves Christians aren't followers of Christ."
3. Often overlooked, but extremely significant to sustaining Christian self-righteousness, is the fact that many, many, many people have been hurt by things they associate with God. Sometimes it was how they were treated by a single person from church. Sometimes it was having a less-than-loving father (the image of whom we, by nature, project onto God). Sometimes it is because they have come to believe God wants them to do a list of things and never do another list of things, and grow in self-condemnation (since
no one can succeed at this in their heartfelt actions without God's help). In the end they have a powerful connection between seeking to know God better and increasing the pain of their self-condemnation. i.e., knowing God better = knowing more rules to be followed and fail at. This is SO much not what God wants for us, I'm not even going to get into it, because this long post would turn into an epically long one.
Jesus replied: “ ‘Love the Lord your God with all your heart and with all your soul and with all your mind.’ This is the first and greatest commandment. And the second is like it: ‘Love your neighbor as yourself.’ (Matthew 22:37-39, 1984 NIV)
