The fact is that two non-Catholics who get married, are truly bound to each other - spiritually even. This is because of the nature of marriage - the vows that a couple makes to each other are not merely legal, they create a spiritual reality. Even when marriage is not a sacrament, it is still a truth that transcends the legal documents of the state.
When a person is baptized Catholic, (s)he becomes bound to another set of laws. Through the authority that God himself gave to the Church, a person bound by the laws of Catholicism through baptism, is not capable of creating the spiritual reality of a true marriage unless they do it within the laws of the Church. This is true whether or not the Catholic person wishes to be Catholic anymore. When you are baptized, you gain the rights of baptism, but you also take on the responsibilities, and this is permanent. It is truly sad, as another poster said, that children are brought to be baptized by their parents and then not raised in the faith. Their parents are binding them to the laws of the church, but completely failing to prepare them to do so. This sad fact mitigates a person’s guilt, but it doesn’t change the reality - that if they are Catholic (at even the most minimal level), and if they do not follow the laws of the Church re: marriage, then they are NOT truly married - even in the sense that two Muslims or Jews would be.
The fact that the marriage is invalid (or more frankly stated, NOT a marriage at all), makes it problematic for a Catholic to support. How can you be support a person in a sham? Even though the couple may have no idea, it is still not something to be happy about. It is really sad, and presents a major dilemma, because the couple in question may not have ever been given the opportunity to know, and act on the truth. The fact is that a person who is Catholic, but who is not prepared to live as one, is not ready to enter into a marriage - which is one of the foundational institutions of Humanity, set up by God specifically to create souls and to get them ultimately to Heaven. Unfortunately, such people (the ones whose parents neglected their religious upbringing) have been terribly wronged by their parents, and have in effect, been disabled by them. We should not be angry at the Church for having rules, or at faithful Catholics who recognize them, but at the people in the children’s lives who have set them up as unable to properly marry and raise children. What a terrible thing to do to a person! This issue can not be isolated as just a “marriage” issue. It is much bigger than that - marriage laws just happen to be one of the more obvious problems that arise because of the loss of faith of a culture.
I wouldn’t bring my own children to such a wedding - it would likely cause moral confusion for them - but I would seriously consider attending myself, at least if not attending would cause a rift. In a case of completely unchurched Catholics, it could be more helpful in the long run, to maintain (or grow) a relationship with them, in the hopes that you can be a positive influence on them and in the hopes that you might help them one day become interested in their faith. That said, I wouldn’t WANT to attend, and if it was out of town, or if there was another way I could avoid it, I might very well. Because I wouldn’t be able to honestly support it, and I don’t like to lie.