Keep in mind, this is a new Gilded Age. Trump would most certainly call in the Pinkertons for some good ol' fashioned strike breaking.

Not an option for most, I'd wager. Federal employees are free to unionize, however it is a felony crime for a federal employee to strike against the government. Furthermore, it's a felony to even assert that this is right you have, or to join an organization which asserts that right. The government's HR department, the Office of Personnel Management, is able to bar any person who violates these provisions from federal employment for life.

Laws more or less to this effect have been on the books since the 40s and 50s, but the issue came to a head in the early 80s when thousands of air traffic controllers went on strike against the FAA after contract negotiations fell through. Reagan ordered the controllers back to work, and, when they refused, summarily fired them. Where they couldn't be replaced be scabs, he activated the military to fill in, citing national security. According to the last article I read, of the 13,000 striking employees, 11,000 were fired and barred from future employment (though I think Clinton rolled some of that back in the 90s).

Considering it's clear that the GOP benefits from government dysfunction, and does everything they can to erode public faith in institutions, striking postal workers would be a gift served on a silver platter for them. Trump will giddily fire every last one of the strikers, be praised for being a big strong man who doesn't negotiate with plebs, and the postal service will be de facto shutter, even if it still exists in as diminished a form as they can get away with while still satisfying whatever requirements there are to have such an institution.

Obviously striking always carries risk, but asking someone to almost certainly throw away their livelihoods for a course of action that will likely only accelerate Trump et al.'s goals is unreasonable.