This article will be filled with a lot of opinion. I am not a statistician and I don't have concrete answers or the background to say this is fact filled. This is a mixture of numbers I have seen (if I reference them I will link to them) and my own thoughts. It will likely sound a little like pseudoscience because it's just my thoughts. The point is to try to open your mind to the possibility that things may not be as they seem on the surface or that they are not necessarily the full picture.
I am focusing on the US because it's simpler and the climate I am most familiar with. This report How Many Adults Identify As Transgender In The United States? says that around 0.6% or 1.4 million people in the US adults identified as transgender. That number is double what was reported 10 years prior. This report New Estimates Show that 150,000 Youth Ages 13 to 17 Identify as Transgender in the US says that 0.7% or 150,000 teenagers ages 13-17 identified as transgender. Both of these reports vary heavily by state. It shouldn't be surprising that more populated and more progressive states have more people self-identifying as transgender.
Looking at that data many people would say there is some reason that more people are identifying as transgender. If you have a bad opinion you might liken it to an over-diagnosis and epidemic (similar to mental illnesses or disorders) or something in the water. Since I am clearly not in that camp, being that I am transgender myself, I think there are multiple reasons for the increase that have nothing to do with just the increase in population.
The first is the collection of the data. Data can be collected in different ways. For example, you can get all the data that doctors and clinics and therapists have. Any patients who are newly prescribed HRT medication for transgender related reasons or data on bottom surgeries on transgender patients. I don't have a medical background. I don't know how connected any of these systems were or are now to be able to give this data. I don't know that they even can give that data with laws like HIPAA. I do know that it exists though and that at least some of it can be used. This isn't foolproof though. It may not capture the full count because of how the doctors' classify the data. For instance, they may not include transgender as a parameter for patients that have HRT prescriptions and there are patients on HRT that are not transgender (menopausal women, people with endocrine disorders). Another issue is that not all transgender people get surgeries. Maybe they can't afford them, maybe the risks outweigh the benefits, or the surgeries are not mature or aesthetically or functional enough to warrant them. I have read that reports on surgery data significantly underrepresenting transgender men because of some of these reasons. If I and other lay-people can think of these issues then I have to assume that researchers can as well. Maybe that means the data is incomplete or the best available, not wrong or nonfactual.
Another way to collect data is self-reporting studies. Again these are highly variable. Depending on the wording of the question you can get different results. I am not saying the data is invalid but that better or more standardized questions would go a long way towards getting accurate results. Since we are talking about the US, just having all the states use the same question would be an improvement (I think that they are/were not according to one of the reports above). Putting aside the question text though. There is still the issue that this data is self-reported. There are people who will not answer questions truthfully, whether by choice or not. For example, geographic location (California vs N. Carolina) may play a significant role in if someone feels safe answering this question truthfully. Additionally, some people may not realize they are transgender at the time and answer incorrectly. Some people will consider themselves not transgender after they have transitioned and are stealth (or whatever parameters they would like to use). That doesn't mean that they are not transgender anymore (in my opinion they are but it's not my place to tell people what they are or are not). Essentially skewing both (cis/trans) numbers at the same time. That might be statistically irrelevant or it might not, I can't say.
There isn't really a great point here. As I said I am not a statistician and I don't have a scientific or medical background. I just think that maybe the reason that it seems like there are more transgender people than ever is because it's a better place to come out as transgender, better access to information, and better understanding of who is transgender. The number is likely to increase a bit more. I have heard that some people think up to as much as 3-5%. Maybe that is a gross overestimate but I think it's entirely possible that the numbers are higher than the research has shown so far.