If avoidance of contraception is supposed to be part of your faith, then what we have here isn't "faith" at all -- and I'm not sure it's "practicality" either. I'd call it "hedging your bets" and I don't find it admirable.
If I had ever gone to work for that institution, I would have paid for my own contraception. A Catholic institution doesn't pay for that. Some employers don't provide free parking. Some give you the day off for your birthday, some don't. There are tradeoffs in any job situation.
As it was, there were certain things my employer-provided insurance didn't cover when it came to my children's health care. If I considered those things worthwhile and necessary, I paid them myself.
I thought that was what responsible adults did.
I do have a moral objection to the government forcing a Catholic institution to provide contraception when it is against Catholic doctrine, even if it's not against mine. I'd feel the same objection to the government forcing a Jewish institution to serve ham, bacon, and sausage in their cafeteria, or forcing a Baptist institution to serve alcohol.
I also have a really hard time with people who have spent a lifetime screeching about keeping Government out of their bedrooms, or off their bodies, now think it's OK for the Government to intrude in the church.