I've tested most of the answers here and there's always some issue with the Timezone, Locale, or when start of the week is either Sunday or Monday.
Below is one which I find is more secure, since it relies on the name of the weekday and on the en locale.
let startDate = start.clone(),
endDate = end.clone();
let days = 0;
do {
const weekday = startDate.locale('en').format('ffffdd'); // Monday ... Sunday
if (weekday !== 'Sunday' && weekday !== 'Saturday') days++;
} while (startDate.add(1, 'days').diff(endDate) <= 0);
return days;