I can understand where the midwives are coming from - it IS their job to give you the best birth possible so I can understand that they would feel threatened by a doula.
Actually, I have to say that I disagree: I can't understand why a midwife would be threatened by a doula. I do agree that a midwife's job is to help a woman achieve the best birth possible for her. Absolutely. The majority of midwives I have worked with have been excellent, they understand the With Woman concept (that's what 'Midwife' means) and the reason they are positive about doulas is because they understand so well what enhances birth - and the continuous emotional support of a familiar, known and SELF-CHOSEN support person really does. This is why several obstetricians I've worked with are also positive about the presence of doulas. It's nicer for all if the birth goes smoothly and the expertise of obstetricians is only called for when necessary.

Midwives are aware that in our current system, the one-to-one care that is safest and best for women, and more satisfying for midwives, is rare, because midwives here are not empowered as autonomous professionals to the degree that they in other countries (yet). Therefore, it is not always possible for a midwife to follow-through a woman throughout her pregnancy, labour, birth and post-natally - although that is what many midwives would prefer (case-load care). Midwives also know that they cannot always be with a woman throughout the labour. They may have other patients to care for, or they may need to go off duty at the change of shift. A doula, however, is not employed by the hospital but by the woman and her partner - so she is able to stay with the couple the whole time.

I've had some great experiences of doula-miwife harmony, and very warm feedback from midwives who have seen the difference a doula makes. (One of the nicest times was after our client joyfully gave birth to her baby in the birth pool in a Melbourne birth centre - and as we left mum, dad and babe to enjoy some privacy, myself and two midwives had a spontaneous celebration hug/dance outside in the hall.) You're right - a good doula will always do whatever she can to work towards a harmonious relationship & good diplomacy between all people involved in the birth. But her first loyalty and responsibility is always to the mother. Most of the time, and ideally, these two concepts are intertwined.

I have had a few occassions in which hospital staff have been dubious or hostile towards doulas. And I have to say - in my experience, an environment that is hostile towards doulas tends to be one that is also hostile towards birthing women in general. When the control of caregivers, and their "territory" or policies, or procedures, or preferences, or legal safety, or not getting flack from the Higher Ups matters more than this woman and this baby's individual welfare (emotional and psychological, not just physical), that is not an environment conducive to normal birth. Fortunately environments with vibes like this are rare - but they are out there and that's where each woman's choice, street-smarts, gut instincts, assertiveness and self-preservation must be drawn on to make good, safe, choices to set ourselves up for the best chance for a good birth experience.

So I would be wary of careproviders who are threatened by doulas in general.