So does this game now start up without crashing, even without an internet connection? I was about to purchase but if I can't even start the game…

Maybe. For some users, such as myself, the answer is no, it will not start without crashing. For other users, the answer appears to be yes, it works fine. I have not found the conditions that would let me determine which group you will be in.

Thanks advowson, I appreciate the reply. Since the crashing happens because of some dial-home issue, I'm not inclined to find out whether I'll be the next lucky consumer.

Yes. Sins of a Solar Empire: Rebellion v1.90 is completely broken for me, just as v1.84 was. The fault address is different, but it still crashes on startup. Context for v1.90:

CS:0023 SS:002b DS:002b ES:002b FS:0063 GS:006b
EIP:00438216 ESP:0033fc74 EBP:0033fcdc EFLAGS:00010202( R- -- I - - - )
EAX:00000000 EBX:00000000 ECX:008044e4 EDX:00000000
ESI:00804a98 EDI:007a47f8

Stack:
0x0033fc74: 0042d8f4 001d15f0 0042d8b7 00000001
0x0033fc84: 00487bdc 007a47f8 0033fcf3 7eb4de40
0x0033fc94: 0033d688 00c3a7f0 bf800000 bf800000
0x0033fca4: 0043fe09 0033fda0 7eb4de40 0033fcf3
0x0033fcb4: 00960a5c 00874710 00000639 0043f694
0x0033fcc4: 00812994 0033fcf3 7eb4de40 00960db8

The fault is still an attempt to read from a null pointer. The fault occurs before the splash screen appears. The game displays a Windows message box with a path to a dump file. The file is tiny: 2661 bytes.

Test procedure:

Start Sins-v1.83 to confirm that no system updates have rendered the previously-working game broken. Sins-v1.83 starts correctly. [Recap for those who joined the thread late: Sins-v1.83 runs fine; Sins-v1.84, Sins-v1.85, and Sins-v1.86 all crash at startup. Newly released Sins-v1.90 is under test.]
Attempt to install Sins-v1.90. Fail because the installer assumes that all the space occupied by the existing Sins-v1.83 will remain used, and thus the drive would not have enough space. (In reality, the installer would have overwritten/replaced these files, so they should not count toward the space required.)
Remove Sins-v1.83 from the system to satisfy the installer.
Run installer.
Start Sins-v1.90.
Crash.

Installed from (sha256 sums):
8290096ec699579b95f5870c7c35d84a9899789783bef1e642a0212b4aff913e setup_sins_of_a_solar_empire_-_rebellion_1.90_(11025)-1.bin
e6596f511ca3faec8d5df41298ed7263f07262cd4de3bbc40a120797ecaa961b setup_sins_of_a_solar_empire_-_rebellion_1.90_(11025).exe

If there is more useful information I can provide, please ask. I would like to see Ironclad actually fix this game so that it can be played. I just have no patience with the GOG support desk, who have demonstrated their absolute certainty that all problems are the user's fault, and cannot possibly be a defect in the underlying product.