To the best of my knowledge, being a vegetarian is not a cause for gyne. There is some controversy about the effects of excess soy intake, but it would have to be truly substantial in order to have any major causative effect.
If you are contemplating surgery, however, you should be aware that vegetarians tend to have poorer healing after surgery because they are frequently protein depleted. I therefore tell my vegetarian patients to prepare for surgery by taking in extra protein, vitamin C and Zinc prior to and especially after surgery. Obviously beef, poultry and fish are good sources of protein, but there can be protein found in vegetables (ie beans, etc) as well. And, of course, there are hi protein shakes.
Dr Jacobs