i sat on a maternity services committee and got to know the matron, head of midwifery and consultant midwife and other useful people via the NCT BEFORE i set foot on labour ward, i think that helped enormously, as it was not a 'tehm and us situation'
I am also extremely careful to NEVER undermine either the MW or my client, i don't make decisions and i ensure i am always respectful no matter the situation.
i have only ever had positive responses and feedback and got a client sent to me by the clinical lead obstetetrician , so i reckon i have done ok 
i have been greeeted with hugs and kisses by midwives who i've worked alongside and get many cups of tea. i've had a lot of MWs insist i do midwifery training, which means i am doing something right !!
one birth i was at recently, it was lunchtime, and the shift leader brought me 3 lunches that were left over!
never had tension or disapproval, but heard of sitations where it had occurred, 9 times out of 10 it is because the doula has tried to make decisions for the woman or force her hand or tried to demonstrate she knows better than the clinically trained people