Coming together to discuss things rationally can work on both a federal and state level. For example, gay marriage was a state issue in the US before 2015, but it was always a federal issue in Australia. The same approach was successfully used by activists in both countries to effectively gain support, however. The UK example re trans recognition, and its lessons, can be applied to campaigns at both state and federal level alike. The point is to bring people together, rather than alienate potential supporters.

Re 'third category', right now trans women are still recognized as no different from cis men in many places, and this places their health care at risk, among other things. Putting them in a third category would be an improvement. Like having civil unions for gay couples is better than nothing.

Re the 'only the genders that are relevant to the law would be covered' part, the law only recognizes the genders of 'male' and 'female'. I personally think non-binary can be included because it meaningfully alters the individual's life in ways relevant to how the law should operate on them, and the government should be required to take that into account. However, while there could be 70+ types of non-binary, they don't need to be individually recognized by law, because they are not relevant to the operation of the law.