I received an undergraduate degree in Sociology but soon after realized I had a passion for finance. I went back to school and earned a finance MBA with a 3.9 GPA from Hofstra University's Frank G. Zarb school of business which is a pretty decent regionally known university and MBA program. I also interned for a summer at a top financial brokerage firm. However, a lot of the job posts I see want a bachelors degree in a quantitative field (i.e., economics, math, accounting, finance). Since I don't have a bachelors degree in a finance related field, will I still be able to apply and attain these jobs with a Finance MBA?

A good rule to live by is that It's often best to avoid applying for jobs that specify skills or degrees that you haven't got.

That said, if you're looking at a job that you absolutely want and are otherwise qualified for, you might try and emphasize certain quantitative aspects of your sociology degree (if you took any math or stats classes - or similar.)