For the most part, you should be allowed to. Any doctor who does not want a husband or a significant other present is probably not someone your wife needs to be seeing anyway.
I went with my wife the first few times to her current gyn when we were first meeting her; also to pregnancy and OB related visits. I do nto go anymore, no interest I guess.
I can say that one issue that health care now is the concern with domestic abuse. In some cases, boyfriends or husbands who accompany their women to the gyn may be mislabeled as abusive spouses; the concern with the med staff is that the woman may be a victim of abuse; the presence of the Boyfriend, for example, is to prevent her from telling a trusted doctor about it.
Some medical practices thus prefer that the women attend appointments alone, so they can include questions about domestic abuse in privacy.
My experience in working in the medical field is that the vast majority of the women out there do NOT want their SO to attend with them anyway. Remember, most women hate this type of exam. Most but not all.
For some men, the idea of another male seeing their SO naked even in a healthcare setting is unacceptable; some doctors who have encountered this would be hesitant to allow others in to exams.
But some women, on the other hand, hate going and will not go alone; if it is a SO or a persoanl friend or family member (like a sister or mom) Some women do not want to go alone and feel more secure with someone they now and trust with them. Medical Staff must be aware of this and accomodating as well.