A lot of the time we use the markers of sex to identify and address inequalities between the sexes eg. education, job roles, pay, access to services, research and statistics, criminal records, social planning. If birth certificates with X became the norm we would effectively lose all the benefits of sex discrimination laws. We would be unable to identify, for example, that girls are under-performing at STEM subjects and thus put in place counter measures. Probably not dangerous for mankind but, since we do not have true equality of the sexes, certainly detrimental to females.
As in your example though, it is essential to know sex in the field of medicine. Disease, illnesses, chemicals and drugs can all effect males and females in quite different ways. We can't appropriately treat or accurately research without recognising biological differences. From giving certain vaccinations only to girls to recognising the different signs of heart attacks in women. I can imagine a time when it is considered unnecessary to do smear tests since cervical cancer rates have dropped so much, not realising the proportion of men in the studies! So, dangerous to ignore sex, yes absolutely, but probably would only adversely affect women.
It is absolutely a feminist issue and hopefully X birth certificates won't become mainstream. Otherwise, add it to the battle list!
What was the outcome of the Canadian case? I'm sure I read that although the child was registered as X, an actual birth certificate would not be issued until the sex was declared.