Much more likely? No, they're actually less likely or just as likely, depending on how you count a mass shooting.

Of those, “the number of known suspects in mass shootings which are trans is under 10 for the last decade,” which translated to “1:880 [or 0.11%] of the 4,400 shootings” they recorded, he said.

The report examined 173 attacks in the U.S. that “that resulted in harm to three or more individuals in public locations,” Justine Whelan, press secretary for the U.S. Secret Service, told Reuters via email, and “three attackers (2%) were transgender, assigned female at birth, but were known to identify as male at the time of their attacks.”

Reuters reported on studies in mid-2022 that found about 0.5% of U.S. adults identify as transgender, and about 1.3% of 13 to 17-year-olds (here).

https://www.reuters.com/article/factcheck-trans-nonbinary-shooter-idUSL1N363273

Either way, it's 97% men being the perpetrators. So any man that says it's trans people needs to look at themselves first.