The worry with going in fast is cold water shock (RNLI, the main UK lifeboats and beach lifeguards). The cardiovascular effects are a particular concern if you get in fast and immediately put in a lot of effort, but the main issue is that even the mildest forms lead to gasping for breath, which can be uncontrollable, and lead to drowning if your face is in the water.
So if you go in quickly, you're increasing your risk. This can be mitigated by ensuring that you don't go right in quickly, but only if the water depth is perfect.
The UK Outdoor Swimming Society's safety tips include "Enter the water slowly, be wary [of] the gasp reflex"
Based on that, and what works for me, I wade in fairly quickly, splashing my chest and upper back once it's easy, and squatting into the water once any gasping has stopped. It may start again. This is in the context of somewhere beach-like and needs to be adapted for steeper entry.
Note that acclimatisation can help a lot, but it takes a lot to be acclimatised, like open water swimming several times a week. Even regular cold showers can help, but in my experience only go a small way.
Some indicative numbers, noting that individual responses vary a lot:
I'm an occasional outdoor swimmer so never get truly acclimatised. In summer (15--16°C or 60°F) getting in quicker - but still cautiously - works for me compared to colder times of year (10-11°C or 50°F is the coldest I've done without a wetsuit, at 5°C/41°F even with a wetsuit the gasping took long enough to stop that my hands were already going numb).