Isn't this a fundamental problem with consequentialism? If you can convince yourself of a serious enough consequence, you can do whatever you want. Steal, hurt, kill. As long as your actions lead to a .000001% chance of preventing Skynet from taking over in the year 50000 AD, any means justify those ends.

How is that something that can be seriously engaged with? Other than trying to talk some sense into these people about limiting their EA calculations to a reasonably observable time-space continuum?

I always felt the problem with consequentialism is that outcomes are uncertain, whereas actions are not. Therefore you are not guaranteed that an immoral action (means) will result in a beneficial outcome (end).

For instance, you push someone in front of a trolley to save 5 lives, but the trolley isn’t stopped and you end up with 6 dead.

That's essentially Kant's argument as to why you should have universal morals (see the classic not lying to an axe murderer).

If curing cancer for the rest of humanity now and forever required knowingly experimenting on and absolutely killing a certain number of people now, how many people could you justify with an Effective-Altruism ethical framework?

Depends on your expected remaining lifetime of the human race? (since from that you might compute the expected cancer deaths over that time and then you can do a simple comparison)

Longtermists simply assume we will harvest Hawking radiation for hundreds of billions of years after the heat death of the universe.

Not meaning to be inflammatory but the same scenario exists in flipped terms: how many people would you let die of cancer rather than, idk, eat the downside of running riskier experiments.

There’s no privileged neutral really. Consequentialism just owns that. Now, that might be a separate question from whether society should act as if there’s a privileged neutral (ie be nonconsequentialist).

Isn’t the inverse more, there will never be a cure for cancer, so how many people can you justify killing to confirm that?

All I know is that when humanity faced the decision with respect to WWII medical experiments , the decision was made to not utilize the data, regardless of potential benefits.

I wouldn't say they ignore it, but rather they categorically have decided that is an unethical justification. E.g. it doesn't matter if experimenting on patients without their consent saves more lives in the future, it is still wrong. Perhaps you might argue that this is an absolute position they can't really hold to for everything. But I think people prefer to find other ways to justify such cases.

You can take 10 healthy organs from one person without any social connections and use the organs to save 10 terminal patients.

See the problem with utilitarianism?

Unlike other hypothetical examples given here (Skynet, cancer cure), this scenario is possible today.