I think every woman is different, and you have to find the right BC pill for you and your diabetes (if you try one, and hate it because it makes you moody, or makes your periods worse or makes your blood sugars crazy - don't give up immediately, just ask to switch to a different one). I've been on loestrin for a long time, and just to try a different option I switched to a pill that also contained progesterone hormone. Then, my blood sugars were absolutely crazy for the next 3 weeks...until I hit the "off week" on the pill pack, and everything normalized. So, luckily it only took one month for me to realize that type of pill doesn't work for my diabetes, and I switched back to Loestrin. But I asked my endo about this progesterone hormone that gave me issues, and she said she's never had another diabetic complain about it, and has plenty that use a progesterone-containing BCP. We're all different, and you have to find a pill that works for you.
I've also used different generics of the same brand (various generics for Loestrin - with the SAME active ingredient) and had very different outcomes - one generic was causing me to get periods every 2 weeks, and awful cramping, and I switched to a different generic (again, same active ingredient!) and I get little to no period each month, with no cramping at all. So you really have to explore your options until you find a pill that makes you feel good! If you can find a good OB/GYN who is aware of your concerns/diabetes, they'll help you find the best option for you.
I've never heard of a doctor not prescribing a BCP because of diabetes - I've actually had endo's that aren't happy if a T1D isn't using BC to prevent unplanned pregnancy (if you're in an intimate relationship)! I suppose they think that an unplanned pregnancy is a higher risk for a diabetic than the hormones in contraceptives. If your OB/GYN is resistant to let you use BC simply because of diabetes, perhaps a second opinion is a good idea.