Filtered colimits commute with finite limits in any Grothendieck topos. A Grothendieck topos does not need to be locally finitely presentable; the presentability rank of a topos is tightly related to the structure of its site presentation, as shown in Prop. 5.5 of the preprint

Gabriel-Ulmer duality for topoi and its relation with site presentations, arXiv:1902.09391.

Indeed I must confess a conflict of interests, as I am one of the authors of that preprint.

Filtered colimits commute with finite limits in any Grothendieck topos. A Grothendieck topos does not need to be locally finitely presentable; the presentability rank of a topos is tightly related to the structure of its site presentation, as shown in Prop. 5.5 of the preprint

Gabriel-Ulmer duality for topoi and its relation with site presentations, Ivan Di Liberti and Julia Ramos González, arXiv:1902.09391.

Indeed I must confess a conflict of interests, as I am one of the authors of that preprint.

Filtered colimits commute with finite limits in any Grothendieck topos. If the site is not finitary, its corresponding topos of sheaves will probably not be loc. finitely presentable.

Filtered colimits commute with finite limits in any Grothendieck topos. A Grothendieck topos does not need to be locally finitely presentable; the presentability rank of a topos is tightly related to the structure of its site presentation, as shown in Prop. 5.5 of the preprint

Gabriel-Ulmer duality for topoi and its relation with site presentations, arXiv:1902.09391.

Indeed I must confess a conflict of interests, as I am one of the authors of that preprint.