I have been fortunate to be able to participate in local small town groups and big city transgender groups too. BTW I have not seen them called transexual but rather transgender support groups. For some people the terms have important distinctions.
I really appreciate our local group as it features everyone together. We share support with all genders, youths, allies and significant others. Hearing from a trans man's perspective or an SOs view point is helpful for me to understanding a wider perspective. Our local group will sometimes split up if there are enough SOs that want to share. When I go to Portland the groups are separated into women and men and the size of the groups may make that more needed. I have been to groups where a couple of people were "observers". I am Ok with nurses and other professionals but very uncomfortable with cisgender straight missionary types attending for what I believed were spurious reasons like evangelical recruitment.
The groups I know of are all "peer support" groups in that none of us claim to be facilitating as a professional therapist but as someone like yourself. We have had family members often come along in support and gain a better understanding of the range we might represent. We start with a preamble that assures we are pledged to confidentiality and some people use only a first name. A facilitator is trained and vetted but we are human. I remind attendees that we allow those with "burning issues" to start but we go around the room so all have a chance to share or not.
There is often a very nice mix of new comers and old hands, minority people and diverse folks of all kinds. We often go out for drinks or fun after group. Groups can lend a sense of community and caring to people in need. Some people come just once and thats it. Others may need a lifetime of support? I wish there had been something like this around 20 or more years ago! And then, there is no better time than now

Join in, it is what we make it!