Even so, a Rand Corporation study released last year looked at the impact of transgender people serving in the U.S. military and found "the number would likely be a small fraction of the total force and have minimal impact on readiness and health care costs."
The nonpartisan think tank's study was originally sponsored by the Obama-led Pentagon at a time when the military was looking at the transgender issue.
"We identified that less than 0.1 percent of the force would seek the type of treatments that would affect their ability to deploy," Agnes Gereben Schaefer, lead author on the study and a Rand senior political scientist, said in an interview Thursday.
According to Rand estimates, out of the U.S. military's 1.3 million active-duty service personnel, between 1,320 and 6,630 members of the force are transgender, but "only a small portion" of them would likely seek to have transition-related treatment, according to Rand.
Rand estimates that between 29 and 129 active service members would seek the transition-related care that could impact their deployability or result in additional health-care costs.
"To put that in perspective, in 2015 in the Army alone there were about 50,000 active component soldiers who were unable to deploy," said Schaefer, pointing out that the reasons were due to accidents or issues unrelated to transgender surgery.
As for Trump's assertion of "tremendous medical costs," that doesn't appear to be the case when looking at Rand data.
The think tank estimates transition-related health care for active service members would cost the military between $2.4 million and $8.4 million annually. That equates to a 0.04 percent to 0.13 percent rise in the active military's $6.27 billion in annual health-care expenditures.
Assuming the high-end estimate provided by Rand, the military's costs of transgender health care over a 10-year period would total about $84 million.
But opponents of transgender people serving in the active U.S. military claim the costs over a 10-year stretch could run into the billions.
The Family Research Council, which identifies itself as a Christian public-policy group, estimates the potential 10-year costs of transgender individuals serving in the military could "total as much as $1.9 billion to $3.7 billion."
Similarly, Republican Rep. Vicky Hartzler of Missouri said the 10-year cost would be about $1.35 billion. Her estimate includes active duty, National Guard and Reserve members, or a force of 2.13 million personnel.
"Our military is the most effective, efficient and well-funded fighting force in the world, and as the president notes, we cannot burden our armed forces with the tremendous costs and disruptions that transgender in the military would entail," Hartzler said in a statement Wednesday. She recently introduced an amendment in the House that seeks to bar the military from paying for transgender surgeries or allowing those individuals to be deployed.
Democratic Rep. Joe Kennedy of Massachusetts, who serves as chair of the Congressional Transgender Equality Task Force, blasted Trump's transgender ban on Wednesday and said on the House floor that transgender service members "are willing to sacrifice their lives to protect our freedom" and "deserve better" from the president.
Rand's Schaefer said they also looked at transgender impact on the Reserve force but the analysis found "it's hard to figure out how the Reserve component members might utilize their health benefits because a lot of them have civilian jobs."
Finally, Rand's research included looking at lessons learned from 18 other countries, including Canada, that have allowed transgender personnel to serve openly in their military.
"None of them reported any negative impacts on operational effectiveness or operational readiness or cohesion of the force," Schaefer said.
The Canadian Armed Forces, in a statement provided to CNBC on Thursday about the transgender issue, said: "Diversity is viewed as a source of strength and flexibility, plays a pivotal role in making CAF a modern forward-looking organization, and is imperative to the CAF's operational effectiveness."
That said, the Canadian military said it does not collect data on the number of transgendered personnel in its forces and has "no bona fide work-related reason" to do so.