Yes and no. It's kind of subjective. Yes, they are the largest single customer, but not the majority of their income. I think about 40% of their revenue comes from the .gov side of things, but they are pretty much the cheapest (and most reliable) company in the game outside of China. China is marginally cheaper, but not as reliable. So, SpaceX gets the lion's share of commercial launch contracts from the private sector.
Anyway, they still hold the commercial resupply contracts for the ISS and the Commercial Crew still has flights to go, but they are doing it cheaper and quicker than the competition. The next round of those contracts are coming up somewhat soon and obviously, someone saving the government a few bucks, well, we just can't have that.
If the .gov was stupid enough to cut off contracts to him and go back exclusively to ULA, Boeing, Northrop, etc, he'd have a shortfall, but I can flat guarantee you he'll come back stronger in another location and focus entirely on the private side of things and make a killing. SpaceX already has their first
commercial manned charter going up along with another being planned for Tom Cruise to visit the ISS for a Mission: Impossible movie or something. Right now, they're the only US company capable of manned spaceflight until Boeing un-****s itself and gets the Starliner flightworthy at almost double the cost of what SpaceX did it for faster than they did.
Of course, Jim Bridenstine, former Director for NASA, loved SpaceX, so, by proxy it's a Trump thing, meaning the Biden Admin will probably kill contracts to them even though they're the only ones producing services cheaper and quicker than the traditional Big Boys. They are
about that stupid.