Question

In the column about appointing women as rabbinical judges, you wrote that it is possible to rely on minority opinions in pressing circumstances, when an important value like equality is at stake. 
I’d be glad to hear more examples: 
Regarding equality, in what other cases can one rely on a minority opinion when we are in a pressing situation? 
What other values that have only solitary textual support (beyond equality) would override a halakhic ruling decided on the basis of the majority?
 
More generally, are there topics in which minority opinions would not override Jewish law even in pressing circumstances (a serious dispute)?