Legal Definition of "Religion"

Hello! I'm giving this question a shot here, hoping to get a little more information before my fiance and I head off to the courthouse tomorrow.

In Wisconsin, where both myself and my fiancé live, there is an option to have a Self Uniting Marriage. According to Wisconsin Legislative Documents, which I found here, it states that "The 2 parties themselves, by mutual declarations that they take each other as husband and wife, in accordance with the customs, rules and regulations of any religious society, denomination or sect to which either of the parties may belong."

When I went to ask questions about this option for marriage, I was told that because we are Atheist, which isn't a religion, and that statute says "Religion", we are not able to preform such a wedding.

After asking the r/atheism subreddit, I was directed to this Supreme Court ruling, where is states in paragraphs 7 and 8 that non theistic beliefs count as religion, in a legal sense.

We are going to be heading up to the courthouse tomorrow with the link above printed out and highlighted, to see if they will allow us to preform this wedding, but we are always looking for more information or better documentation to help us so we can tie the knot in a way that means something to us. I just hate the fact I was told I was not allowed to marry my husband the way I want to because I do not believe in a god.

My fiancé and I thank everyone in advance for any and all advice given. Thank you so much and have a wonderful day/night!

-Courtney and Taylor