Yes Wicca is a recognized religion in America. But that doesn’t mean all pagans should be grouped under that term, just to have religious rights.
My path personally has no relationship to Wicca, aside from the fact that I studied it for years in my teens years before I learned it wasn’t for me.
For me to claim the religion as my own would be would be wrong.
I claim no religion beyond the grouping under the term pagan. I am pagan. I am spiritual. I am a witch. I go where I am guided, without the rules of religious dogma.
Many people who identify as Wicca have similar views, but the fact remains that their is something about the religion that draws them to associate it.
If someone chooses to use that terminology to label themselves, perfect. But the assumption that we are all Wiccan is false.