Unfortunately I cant speak to your workplace relates concerns. I live in a state that have gender-identity nondiscrimination laws. Fortunately though youve got some advise from other folks around this!
What I can speak to, however, is your familial concerns. Almost in the exact same boat as you, I came out to my mother and sister first (my father and mother are divorced and was welcomed with open arms from them) and felt the most anxiety/fear about coming out to my father who is also a huge bigot. To make a long story short, unfortunately in my case, I came out about my transition and wasn't accepted by my father. One of the biggest things i learned was that I had expectations of acceptance because i assumed since im his only blood-related child Id be unconditionally loved. In retrospect, this ultimately made me feel worse. Had I gone in without expectation and just the acknowledgement that I was coming out for ME and me ONLY, the blow would have been significantly less.
It does feel scary and does suck when a parent doesn't accept whatever you feel is your true self but don't let your self-worth be contingent on someone else's views of you. Be prepared to be unaccepted because its a real possibility but also remember that he isn't the be-all end-all to the love you get from other family members. You have your mother and sisters and focusing on the support and love you have from them rather than the support and love you may not get from your father may help you the best in this situation.
Sorry for a wall-o-txt! Also this is just me speaking from my experience and not meant to dictate what you should and should not do or think! More of a food for thought, i suppose (:
Nevertheless I wish you luck in your coming out process. It can be scary and hard but you can do it! Once its all said and done its a relieving feeling better than any other no matter who doesn't agree with you along the way! -- coming from a kid 4 yrs on T! :D