Since some people might still not have seen it, I'll repost it here:
https://www.dropbox.com/s/693fimgtcmxvxpa/fo_new_vegas_gog_winxp_fix.7z

If you replace the GalaxyWrp.dll in the game's folder with the one above, the Windows XP compatibility that GOG broke will be restored and Galaxy functions deactivated.

Origin and content:
https://www.gog.com/forum/general/release_fallout_new_vegas_ultimate_edition_1c381/post153
https://www.gog.com/forum/general/good_news_galaxydll_breaks_xpcompatibility_in_good_old_games/page1

What exactly this fix is is explained here for those wondering :
https://www.gog.com/forum/fallout_series/fallout_nv_no_drm_still_compatible_with_windows_xp/post8

This does not work; all it does is cause the launcher to act like FONV is not installed; game will not launch directly from shortcunt either.

It did in 2017.

I was having crashes that I couldn't figure out after talking to Doc Mitchell and refusing hardcore mode, and also after making purchases. Swapping these files out fixed everything. And I'm running Windows 8, not XP.

I think I figured out what was going on: the game was crashing because of GOG achievements. After I applied this fix I realized that buying the ammo I was trying to get was giving me a bartering achievement.

I'm using the "offline backup installer" version which is probably the root of the problem. That they didn't test it, I mean :-/