You would be wrong. My nephew is in Special Forces (Green Beret) They were mandated and all received vaccines. No questions asked...Maybe, Though I doubt SEAL Team Members and other specialists would fall into that group.
If the vaccine isn't offering protection from infection, how does the mandate argument not fall apart?
"Davis Younts, an attorney representing dozens of troops who are seeking religious or medical accommodations for the vaccine mandate, said that most of his clients are not going to comply with the mandate even if they aren’t granted an exemption. “My clients, the guys I’m representing, and the SEALs I’ve spoken to, are what we’re calling ‘hard no’s’… that means you’re going to submit a religious accommodation request, you’re going to submit a medical exemption based on where you’re at… and then if it’s not approved, they’re not going to take the vaccine.”
https://dailycaller.com/2021/10/11/pentagon-military-vaccine-mandate-seals-navy-coast-guard/