It certainly is a communication barrier. It may not physically dampen your ability to hear a doctor, but it is a psychological barrier in forming a relationship. Non verbal communication is vital, and there is tons of evidence suggesting how important its role is in forming a relationship, especially facial expression.
As a doctor you have to make very important decision for and with your patients. You perhaps see them for a 20 minute clinic meeting every 6 months, so it is vital you don't slow the process of forming a relationship with your patient by garnishing a physical barrier. It is important to remember that we have an elderly population and they take up most of our medical services. Whilst your average 20 something may not have a problem with a doctor in veil, many people in their 70s and 80s who are from a completely different generation will do.
Hygiene is an important consideration; we have to be bare below the elbows these days with nothing that will dangle about. If I can't wear a watch or a tie in a clinical setting then I find it outrageous that special exception is allowed for others when it is in direct opposition to best clinical practice. Bearing in mind how I despise looking scruffy (would love to wear tie and jacket) and having a watch is bloody useful for counting a pulse. Is it a hygiene risk? I'm not sure, but there isn't the evidence out there to say it is hygienically safe that is for certain. You cannot assume it is ok until the evidence is there.
We have to make sacrifices as doctors for our patients, and appropriate dress is another one of them. If you aren't happy to respect your patient's needs and what's in their best interest then there are plenty of other careers out there.
I've never encountered a doctor who does or wants to wear a full veil, so I don't think it's that big of a deal. But from a position of best medical practice, and as a matter of principle, I think it is unfair to make a large proportion of your patients uncomfortable on a daily basis due to your own unwillingness to adapt to the dress code of your workplace, or the unwillingness to choose a career where you can have the freedom to wear what you want.
There is no need to force clinically damaging attire on people in their time of need, especially when it is religiously motivated and not scientifically motivated. Medicine is a largely secular service where decisions are made upon best scientific evidence based practice, and it is important to keep a distinction between your professional duty in the workplace and you private beliefs and practices.