The lack of understanding of what reverse-isms are or are not is telling. Equality is nothing without fairness, and fairness would require recognizing that some systems of oppression exist (against women, against POC) but some prejudices are not systematic ("I hate men", "fuck white people"). The former are the ones we need to remediate as a society, the latter are rude to receive as an individual but will not impact your ability to survive in society.
Systemic prejudices gain their power from their pervasiveness and lack of negative feedback from peers. These newer, less systemic prejudices gain their power from their increasing weight among people in charge due to the perceived prejudice in rebutting them.
To be more explicit, the discriminatory power of a prejudice can be thought of as
Power = frequency*weight/backlash. Being prejudiced against women happens frequently (to various degrees) with a relatively low weight given to such opinions and average backlash. Being prejudiced about cis-gendered or white people or, God forbid, a white cis male, has less frequency but has a huuuge weight given to it. And, as these rules of conduct would enforce, they would have virtually no backlash.
Think about the event at that Python conference a while back. People lost their jobs over a 'dongle' joke. The guys that made the joke didn't even know she was there. If a woman had made a similar joke in reverse, no one would do anything about it. But because they put greater weight on her opinion than theirs, they were severely punished. (In this case there was a backlash against the woman, but only due to widespread media coverage.)
So, I think that you're wrong. We cannot allow some prejudices to take precedence over others. And I think you're wrong because these non-systemic issues will impact your ability to survive in society due to the increasing and disproportional weight given to them. They just happen in different ways. Systemic issues occur as the sum of small harms while non-systemic issues generally materialize as infrequent but more serious individual damages.
That said, I find that this conversation is necessary at all is ridiculous. I'm barely an adult so I find my worldview of society colored by my not-too-distant view as a child, where adults hide things from children and tell us children to get along our we'll be punished.
And it is thoroughly pathetic that with adults can't just fucking get along. I mean, come on people. Grow up. Don't discriminate (but don't be too sensitive as to consider everything discrimination), don't be mean, don't take jokes too seriously, learn to take criticism (but with a grain of salt), and don't attribute to malice what is likely just ignorance.
Just get along, dammit, or I'm telling all of your mothers.