Moving to another, more tolerant place or even dating in a separate place from where a person lives is one set of
solutions. I'm sure they're workable and effective for quite many people.
Nance and I live in a place full of religion, hypocracy, and closed-minded-cookie-cutter monogamy minded people (many of whom have zero sight of ethical anything.) Having been something of a global Nomad on many U.S. Government sponsored adventures, and then being in a civilian occupation that demanded travel, I adapt well. I chose to move here
from Hawaii, when I fell in love with her. I made that choice knowing that I/we might experience some scrutiny. I personally don't subscribe to the policy of people outside of my house having much control or influence over the choices made inside my house or the people who live there. I have a life to live and a family to lead. I choose to live my life proudly and fairly colorfully. People will talk. Who gives a shit? Some of our kids will travel the world. Some of them will never leave this town. None of them deserve to be taught that they don't have the right to be whomever they choose and do whatever they like, regardless of their zipcode, IMHO.
The OP's topic was equality within the relationship. As to that, I think a series of rational conversations covering what your needs are is in order. To me, it sounds as though the wife is making something of a last ditch power play in a misguided effort to "show you her place." Remember, when you bring this up that she most likely is doing this from a place of pain in her. I'm not saying she's a victim. I can't know if she is or isn't, from what you've written here, but clearly she is acting out. I'd read up on Nonviolent Communication skills and maybe consider ways of resolving this in the best, most balanced way for the entire family unit rather than just "demanding" to be "equal." I do hope you find a way to feel better about this. Good luck