[Routine Help] Would Azelaic Acid and Bifida work in the same routine?

I recently got the Bifida Biome Complex Ampoule from Ma:nyo. Normally, I use Azelaic Acid 15% in the AM and PM. I skipped AA last night and only used the bifida ampoule and loved how my skin felt/looked in the morning.

I would like to keep using it but AA has antibacterial properties while bifida is a probiotic… would AA just neutralize the bifida? Has anyone successfully used both in one routine?