Installed mods don't count. Only enabled ones.
You can see this by disabling mods and starting a run, you won't see the little blue mark next to the saves that says "This run has mods enabled"
Of course, you can also look up for "Achievement Enabler" mods.
Or one of the many save files that simply lets you instantly complete an Honour Mode run and earn your Golden Dice (As well as any other achivements you might want, like Jack-of-All-Trades) so you can freely play Honour Mode without care for active mods (Besides any other achievements)
Heck, there's even
Golden Die Unlocker to simply get access to the die.
Really the only jank thing here is that for whatever reason some mods do and some don't block achievements. It's kind of inconsistent.
I know I managed to unlock an achievement while doing a heavily modded run (Extra feats, bunches of extra items all scattered throughout an updated loot table, extra encounters, a ton of extra classes and subclasses, extra origin bonuses, extra spells, reworked feats, like 10 different dependencies to make everything work etc... Basically the only thing that I hadn't changed is character appearances and party size) so the affect of mods isn't super strict. To the point where it would seem to be fairly rare that a mod actually inhibits achievements.