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For my specific flights, I'm flying out of Dublin (Terminal 2) which has US customs pre-clearance. I arrive in Atlanta before connecting to San Francisco. I'd like to shop at the duty free store in Dublin, but I don't want to risk having a bottle of whiskey with me in my carry-on luggage if I need to go through TSA security in Atlanta.

I'm flying on Delta.

You will almost certainly not have to re-clear security - although you can't definitively rule it out.

The vast, vast majority of pre-cleared flights will arrive into their US destination as if they were a "domestic" flight. ie, you will be let out into the departure area of the airport.

Depending on the airport layout you may need to re-clear security in order to get to your departure gate, however in Atlanta all terminals are connected air-side via the "Plane Train" so this will not be required in your case.

Technically it is possible that pre-cleared flights can be directed to arrive into the standard international arrivals area, with passengers being forced to go through US immigration/customs a second time. This is incredibly rare, so the odds of it occurring are very low - but officially it can happen.

From the TSA's website:

Duty Free Liquids: You may carry duty free liquids in secure,
tamper–evident bags, more than 3.4oz or 100 ml in your carry-on bag
if: The duty free liquids were purchased internationally and you are
traveling to the United States with a connecting flight

Just make sure you get a STEB (secure tamper evident bag) which is basically a self-sealing plastic bag that has the receipt in it. All duty free stores will know what they are and have them.

https://www.tsa.gov/blog/2017/05/25/tsas-2017-summer-travel-tips

In my experience, when arriving in the US after a pre-clearance flight, you arrive in the post-security area of the terminal, and can catch a connecting flight without going through security at that airport, assuming that the gate you arrive at and the gate you will depart from are connected post-security.

Pre-cleared flights usually gate at domestic terminals and deplane direct to the terminal as any other domestic flight. For all practical purposes pre-cleared flights are considered domestic flights from a ground operations perspective. It is theoretically possible but quite unlikely that immigration officers might be waiting for one specific passenger at deplaning, but this would be a very rare occurrence.

You may have to change terminals: in ATL this is done via a train that runs under the terminals, but always inside the secure zone so you should not have to go through additional security after deplaning if you have pre-cleared at the point of origin.