Not necessarily. You get the same legal benefits with a civil union, where it's available.

Some people see marriage as a construct of religion and being not religious or against religion, have a problem with that.

Some religions only allow marriages within their own faith, or pressure for conversion, or won't allow marriage within the church, where the families won't accept the marriage otherwise. It means ostracization if the couple go through with it. My cousin was pressured to convert to Catholicism when he got married and was denied a service outside the Catholic church, couldn't even have a Protestant minister co-officiate the ceremony.

Also, when I say non-religious, I don't necessarily mean athiest. Imagine a practicing Luciferian falling in love with a Mormon or a Muslim or a Jew. The Luciferian is practicing a spirituality, but one that rejects Abrahamic faiths and therefore the concept of marriage as a tradition of those faiths. It doesn't automatically follow that he/she would be against a permanent pair bond. They just wouldn't want it tied to a religion, specifically. Whereas, to the religious partner, it may not feel real or "count" within their family and community without that priestly blessing of the vows.

I'd guess that most athiests would just go along with the ceremony to make the other partner happy. They don't believe in God anyway so they wouldn't worry about offending Him or making false spiritual promises, etc because it's just not real to them. It wouldn't even cross their minds because to them it's just a (predominantly commercial) part of coupling.

To be fair, most religious people today think if marriage in those commercial terms as well. It's all about the wedding and the honeymoon. Hardly anyone thinks about the vows anymore.