I wonder if you feel silly mocking religion, after finding out that I am actually agnostic. I am not in defense of Catholicism. I don't care what God thinks of the Catholic doctor. I am in defense of the right for Catholic doctors (who have the right to choose their own values, and I respect that) to make the choice about what services they provide for society.
That service includes providing "abortions" or providing "recommendations for abortions". If we are in a free society, that means we are free to make the choice of what jobs we wish to do, whether that is a job requiring extremely technical skills and labour (abortion), or making a simple statement (speech/written).
Catholic doctors may feel it is immoral to provide information about where one can get an abortion. Hence, good Catholic doctors may feel this is a significant barrier to becoming an obestrician (waste of perfectly capable talent). The onus is on the pregnant mother to find out where she can get an abortion - she has no "right" to force it out of the mouth of the Catholic doctor. She can ask, but she cannot force it. Everyone has to be given choice, if you are pro-choice - you can't steal choice from one person and give it to another, that is socialism.
If you are truly against bureaucracy, let the market find its own way to connect those who are seeking abortions (demand) and those who want to supply abortions (supply).