Lose the gulf stream and the east coast gets a lot colder, Greenland freezes up, England goes from rainy to frosty, Europe gets colder. It would be a serious disruption. But given the source there is little reason to think it has gone that far.

There are credible sources that are well documented, peer reviewed in established journals, that show the flow has been slowing for a long time. Many highlight the expected climatic changes such a loss would be caused by the Gulf stream stopping. Essentially the Gulf and areas near the equator get hotter and the North Atlantic gets colder.

The survival aspects of this comes down to the short term changes with the East coast being hotter in summer and colder in winter with more sudden ice storms and blizzards. The Gulf coast and a fair distance inland along the Mississippi watershed, might be hotter and dryer. Longer heatwaves and more droughts. If there is less rain in the Midwest barge traffic may not have enough water to move. Florida will be between the colder Atlantic and the hotter Gulf. I would suspect it would be hotter and wetter, more tropical. Long term the most practical way to cope will be to move.

Bottom line is that if climate change goes far enough we could lose the Gulf stream and see large shifts in climate that will prove inconvenient and disruptive. this wouldn't alter the degree of global warming. The total amount of energy remains the same, just redistributed differently.

That said, there is little credible evidence here that it has happened, or will happen any time soon.