to close all remaining loopholes that previous experiments on violations of Bell's inequality left open.
When they say closing a loophole, the point is to get better experimental results to verify an inequality predicted by quantum mechanics.
So quantum mechanics predicts an inequality and some imaginary theories (which don't agree with quantum mechanics) don't predict it. The magical theories that don't predict it, disagree with quantum mechanics, and disagree because they have certain ... silly ... features.
They have a fake determinism, specifically they pretend to be deterministic about some things (like objects to be measured) but are explicitly not deterministic about other things (like the devices used to measure things). You can see this directly in Bell's paper when he assumes the theory to be criticised does not allow the hidden variable $\lambda$ to affect which direct the spin is measured.
They are not contextual. Which means the result can depend on the hidden variable and on the orientation of the measurement device but not on the state of the device or even on which device type you use. Despite the fact that quantum mechanics explicitly predicts different correlations between say spin and position when you use actual devices designed in different ways. You see this in Bell's paper when the result is supposed to be a function of just the orientation and the hidden variable of the thing to be measured.
They are local. Despite the fact that it isn't even clear how to specify initial conditions for a local theory.
So the point is that a local and non contextual theory with fake determinism will have one (wrong) result for the inequality. Therefore any that agrees with quantum mechanics will either have to have a real determinism, or have no determinism (and it isn't scientifically possible to distinguish between those two options, only fake determinism has scientific predictions), or must be non local (which means you cam specify initial conditions), or must be contextual (which means you can correctly predict what happens in real devices).
If you want to agree with quantum mechanics you definitely want to be contextual by really looking at actual experimental setups when needed. And you definitely want to be nonlocal so you can specify initial conditions. Determinism or no determinism is up to you, any theory of one type has a theory of the other type that makes the same predictions so calm down and don't worry.
My question is, does this really close the door on any possibility of local realism being true?
No. What it does is close the door on local and non contextual theories with fake determinism.
I wanted to understand whether things have really changed from the standpoint of different interpretations of Quantum Mechanics.
Absolutely zero people wanted a local and non contextual theory with fake determinism. So it's purely academic.
Both locality and realism seem very intuitive
How can local realism seem intuitive? How would you even specify the initial conditions in a local theory? And you can be realist on say position and then to get the correct correlations for contextual measurements you have to realize that anything incompatible with your realist parts is produced by the interaction.
We already objectively know that interactions create spin eigenstates that weren't there before.
Case in point, interact in the $\hat z$ direction first, then the $\hat z$ direction second, then the $\hat x$ direction third. Repeat and note that the second $\hat z$ interaction always agrees with the one immediately before it. So clearly the $\hat z$ interaction puts it into a state that reliably produces a particular outcome for $\hat z$ interactions.
This time interact in the $\hat z$ direction first, then the $\hat x$ direction second, then the $\hat z$ direction third. Repeat and note that the second $\hat z$ interaction only agrees with one before it 50% of the time (of spin one half). So clearly the $\hat x$ interaction changed it into a state that no longer reliably produces a particular outcome for $\hat z$ interactions.
So interactions change things. No complicated measurements required. Realism can not be about an interaction that just passively reveals a property without changing things. Any interaction for two things that don't commute changes things. Full stop.
I know he was a strong proponent of the Bohmian Interpretation and strongly felt that QM would at its core end up being formulated in an observer independent way that would ensure the elements of the theory correspond to actual things in the external world.
Bell spoke often about people misunderstanding him. He indeed liked the dBB theory. And that theory is realist about position, but not about spin. No theory is realist about spin because different components of spin fail to commute with each other so clearly spin interactions change things and aren't passive measurement processes that reveal properties without changing things
I'm very much of the same persuasion,
What persuasion? Clearly if you realize spin interactions change things then you know they aren't measuring something that already existed while failing to change things.
What are the options?
Same as always. Don't use local theories that are non contextual and have fake determinism. But no one does, so that was easy.
Does this experiment mean anything with respect to Bohmian mechanics/MWI/other "realist" interpretations of QM?
Nope. Those theories are designed to predict the same things as quantum mechanics so they were also confirmed by the recent experiments.
And what of this recent speculation into ER = EPR? Does that idea actually suggest that communication could be facilitated through subatomic wormholes, thereby bypassing any worries of nonlocality?
That's a very different question, and should be asked separately.