Several outlets including NPR were reporting last week about discharges of immigrants seeking to join the military, including the Army Times. It appears the development may have to do with the program for Military Accessions Vital to the National Interest (MAVNI), which emphasized recruiting for language skills especially in the Army, according to this Military.com article. A Vox.com article seems to identify security concerns stretching back to the Obama Administration combined with difficulty verifying backgrounds of immigrants from countries with less robust information systems.
Setting aside the impact on individuals for a moment, it is also useful to assess how big of a challenge this is for the military. The MAVNI document above, which appears to have been written in 2015, states that about 5,000 green card holders enlist each year, and that 109,250 have attained citizenship through military service since 9/11.
Active-duty force strength is about 1.34 million, according to Pew Research. It is harder to find the percent who are foreign born. In 2008, when forces were roughly the same size as they are today, there were about 65,000 immigrants on active duty, or about 5% of all active-duty forces, and more than two thirds had been naturalized. Ten years may have changed this somewhat, but these magnitudes imply something like 20,000 green card recipients or around 1.5% of forces.