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USCG Shinnecock has, in the past, sometimes refused to make any comment about conditions there in fear of liability. Honest.
You can find depths in excess of 100' outside the inlet, and shoals of less than 6' in the inlet or inside of it. If you time the run at slack current (current, not tide) it is usually smooth, but if there is any current running, and especially if that is against waves or wind on the outside...the inlet can be impassible, even for the local fishing fleet and the USCG SAR boats.
So by all means, you want local knowledge. the USCG station (if they're talking), the local jetski/boat rental company, the local commercial fishermen...whoever you can speak with. Given good weather and a slack current, you should be able to find the way in without problems. But this is definitely an inlet that breaks boats. Doesn't just ground them, but breaks them if you get it wrong.
I don't know about recent dredging, but conditions there change fast. If you do have to abandon an attempt to enter the inlet, just bear in mind there's no really great alternative without several more hours of sailing. (All the south shore LI inlets can be nasty given the wrong timing and weather.)