It was more stable after the SP2, but initially it was undermined by buggy drivers and rampant malware, NT kernel or not. True, it was better than ME…
What most people remember of XP now is what it became after a couple of years of fixes and improvements, and the contrast with Vista.
It was hailed for its improvements in stability from the time it was released. My recollection was that it was a massive improvement over 98/ME lineage. It was mostly a wash vs Windows 2000.
Yes, it became more stable with the service packs, but it was a significantly more stable OS out of the gates than anything consumer users had been getting.
Rampant malware was a separate (and very significant) issue.