Is today a real weekday?
MATLAB, 53 bytes
d=datetime(input(''));week(d-(input('')=='M'))==d.Day

This answer accepts the first input as a string '2017-02-06' and the second input as a string (either 'S' or 'M').

It constructs a datetime object from the first input and saves it in d. We then compute the week number (but first we subtract 1 day from the date if the second input is an 'M' since week uses Sundays by default) and then we compare this week number to the day of the datetime object to yield a boolean.