Is it permissible to attend a wedding where one of the participants is a non-practicing Catholic and the other is a non-Catholic? If not, why? I cannot seem to find the correct way to explain my stance.
If the Catholic has received from his local bishop a dispensation from cult to marry a non-Catholic and, if applicable, a dispensation from form to marry in a non-Catholic ritual, the wedding will be presumed valid by the Church. If both parties are baptized, the wedding will be presumed sacramental.
If the proper dispensation(s) are not sought and granted, the wedding will be presumed by the Church to be legal (i.e., recognized by the state) but not as valid or sacramental. Should you decide not to attend, there is no need to give a particular reason unless pressed. If you are pressed, you could simply reiterate that you are unable to attend. The only reason why you might decide to give a complete explanation would be if one of the couple was a close family member whose wedding you would otherwise be expected to attend as a matter of family duty.