No one has yet (publically) fielded an antisatellite weapon capable of shooting down a GPS or Galileo satellite.

Low Earth Orbit (LEO) satellites, those in orbits of about 1000km altitude or less, are relatively easy to shoot down. There was an F-15 anti-satellite missile, I believe successfully tested several times. The Soviets had a system where they used a guided bomb placed in the same orbit as the target satellite. They could tail any LEO satellite they wanted and destroy it at their leisure. This was also tested several times.

LEO satellites are important targets because almost all the surveilance satellites, both imaging and radar, are kept as close to the ground as they can, to maximize resolution.

Navigation satellites, on the other hand, are a much different problem. Both GPS and Galileo are in (will be in) Medium Earth Orbit (MEO) at about 20000km altitude. It would require a launch vehicle of almost identical capability to the one which originally launched the target to intercept it. This would mean that shooting down a satellite that high is almost as expensive as launching it in the first place.

Probably if we wanted to shut down Galileo, the best way to do it is by spoofing. Spoofing is a process by which an adversary is able to mimic the signal from a real satellite, but with incorrect information, so that receivers on the ground either cannot compute a position at all, which is bad, or compute a wrong position, which is worse.

The whole point of the encoding on the present military system is to prevent spoofing. The GPS transmits two signals simultaneously, one unencrypted and one encrypted, for military use only. The military code is secret. Any satellite broadcasting a military signal without that military code will be completely ignored by the receiver. In fact, the receiver will not even detect that it is there. Since the code is secret, only the military can create that signal, so if your receiver is able to detect it, it must be authentic. The civilian signal on the other hand, since it is published, can be replicated by anybody and therefore easily spoofed.

The Galileo system has a civilian unencrypted signal, a commercial encrypted signal you can buy access to, and a government encrypted signal you cannot. The civilian signal can be easily spoofed, and the commercial signal also if our military buys the keys.

The american GPS satellites are perfectly placed to act as spoofers, and have all the necessary hardware already onboard, to do their main jobs. It would surprise me a great deal if they could not be programmed to spoof either the russian or the new Galileo system, but of course that capability would properly be kept secret

So if the bad guys equip their weapons with civilian or commercial Galileo receivers, those are pretty easy to jam. If they use government receivers, then one of the governments involved is a conspirator and is committing an act of war against whomever the bad guys are targeting. Galileo does not represent a real threat.

On the other hand, a little competition is a good thing. It may be that the american military will be forced to compete against Galileo by providing a better civilian service, thereby causing everyone to buy american GPS receivers which can be disabled in an emergency. This has already begun by the removal of selective availability, an intentional degradation of the civilian signals, and is continuing in the form of new more accurate civilian signals on the next generation american GPS.

As a patriot, I want my military to have as much control over navigation capability as they think they need. As a civilian GPS user, I want as much accuracy as possible. By providing competition, Galileo forces the american military to improve the second to maintain the first.