The anti-LGBT group filed a motion in support of its application on October 26. It seems that the group literally fear the Apocalypse.
Indeed, in this motion, the Westboro Church says:
"Throughout its years of picketing, WBC has warned Kansas that the sin of homosexuality, and particularly same sex marriage, will bring great woe and harm to this state.
"Today the number one moral issue facing this nation is same sex marriage. WBC has a vital interest in what the courts rule regarding this issue, as it directly impacts their religious practices, beliefs, preachments, picketing, association and speech, as well as the wellbeing of their fellow man."
You can read the entire motion here: http://fr.scribd.com/doc/244524950/2-14-cv-02518-19-WBC-motion-to-intervene