Why, [does] anybody else in the world give a rat's tiny hiney who I marry, who you marry, or whether we marry or not?
It's not that hard to understand when one stops to think about it.
Consider for a moment that marriage is an important contract that governs keystone social relationships in the human species. In particular, think about the historical role marriage has played in foreign relations, diplomacy, taxation, transference of property, granting of title and prestige, pedigree breeding, and so forth. Setting aside these somewhat more dated roles marriage has traditionally had, also think about the sacredness of the contract, the depth of its meaning, the implications it has for social and cultural norms, and so forth.
In short, marriage is an extremely serious business and how it is conducted is not a question to be handled lightly. Different cultural groups throughout history have had very particular and specific standards for it, and with good reason - marriage is a huge vehicle of social relations between humans in ways that have a very strong impact on the entire tapestry of that society. From this vantage point, it becomes more shocking to not care about marriage; being very particular about how it is handled is essential when one recognizes the critical social role it plays in a society.
Why does she think [snip] that it is robbing her of her "religious freedom" to deny soimebody else the right to live their life as they see fit?
I obviously can't answer from her perspective given I don't share it, but as before, if we consider things from a broader vantage point it isn't that hard to understand. All limitations on human behavior infringe upon human freedoms. Doesn't matter if we're talking speed limits, what kinds of marriages are okay, or credentialing who can practice medicine. All of these are social contracts that deny humans the ability to behave in certain ways and represent a loss of freedom to do what you want in exchange for social order. If a particular group doesn't like the social order being created by said limitations, well yeah, they're going to call it a loss of freedom. Because it is... from their point of view.
In any case, personally, I have a hard time celebrating this change. I can celebrate it when the ghoulish remission of women's rights is fixed, and am livid angry that this gets through but basic flipping women's rights can't get through. I know that sounds petty, but... basic flipping women's rights for flips's sake.