No, with regard to your first sentence, as there are mentally and emotionally intelligent people who are not biased but who recognize the word usage oxymoronic quick-fix error being attempted by political factions that would completely disrespect definitive propriety, definitive propriety that forms the foundation of our use of language to effectively communicate perceptions and concepts existing both today and in the past.
Definitive propriety requires that we honor the meaning of words and not try to purposely corrupt their meaning to make them mean other than what they truly mean.
For example, when differentiating between sex-gender, we do not call adult females "men", we call them "women", because if we corrupted the meaning of "men" to include females then the word "men" would no longer be of value as a descriptive word in both the past and present.
Both men and women have the same human rights, however, they are simply named differently.
In your example, yes, both a cat show and a dog show are a show, just like both men and women are people.
As you go on to say, we still call them shows, .. and each cat show and dog show can create the same contests and prizes and the like with descriptions appropriate to the cat/dog show (best purr, loudest bark, best cat in show, best dog in show, etc.). But, the dog show and the cat show are still kept separate and referenced with separate terms.
So when speaking of cat shows and dog shows they are always called "cat shows" and "dog shows" because the compound term is foundationally descriptive. They simply aren't called "shows" when being publically presented and referenced to avoid understandable confusion.
Likewise, we don't call adult females "men", even though the syllable "men" is found in both the word "men" and the word "women".
The word marriage has always been since its inception just before the agricultural revolution more than 12,000 years ago "between a man and a woman as husband and wife". That's what the word means. And comparatively microscopic numbers of occurrences of erroneous applications of the word throughout history from time to time in no way changes what marriage truly is any more than the similarly rare instance of calling a cat a dog justifies entering that cat in a dog show.
But are the committed romantic relationships of same-sex couples any less a domestic partnership civil union than the committed romantic relationships of opposite-sex couples?
Absolutely not, just like cat shows are every bit as ethically legitimate as dog shows.
OS and SS couples' relationships should both be recognized by government and private enterprise.
However, with respect to definitive propriety, the foundational test of words and their meaning, a test that comes first prior to ever speculating whether discrimination has occurred, an SS-couple's committed romantic domestic partnership civil union is simply not a "marriage" any more than a female adult is a "man".
A female adult is a "woman".
Both "woman" and "man" have the "man" syllable.
And thus I have suggested "homarriage" to be the word used to describe the committed romantic domestic partnership civil union of a SS-couple.
You have suggested "same-sex marriage".
It seems to me that the only task left is indeed to create a new word that has meaning here in this case and create domestic partnership civil union statutes in every state and recognized by the federal government so that on the 1040 form etc. there would be added a separate status box called "homarried" or whatever is decided.
When we respect definitive propriety we progress and become smarter.
When we ignore definitive propriety and thus disrespect it, we regress, and dumb ourselves down.