If it's not reflection, then it's refraction. :)
A water material with no reflections will look very artificial. If you want to get rid of fireflies in such situation:
- Most importantly, you will need to render your image for enough time. Fireflies may appear at first, but after ~50 passes they should start converging to a cleaner result. The main reason is that you are dealing with tiny details (often smaller than a single pixel) so you need to shoot a lot of samples.
- If you are not planning to save to a high-bit depth format (like 32 bits), consider using some kind of clamping. You can either add the Reinhard highlight clamping operator to the VFB tone mapping stack, or you can try the Highlight Clamping option in Render Setup > System.
- Consider enabling motion blur - it will simply blur the fireflies.
- You can also try adding some roughness to your water material - it will also "blur" the fireflies a bit.
- Lastly, if you are using an HDRI environment with a sharp sun disk, you can use an overcast HDRI as environment override for reflections and refractions (it won't help if you are using Corona sun though).
