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I think the point they were making was that since we know of weaknesses in certain situations we should avoid using it even in the safe situations so that we can eventually drop it from crypto libraries all together. There are alternatives that we can all move to.

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Let's say I make a hash of an asset and put it into a very long-time archive (like 100 years or whatever). What checksum algorithm should I use to be sure it will be readily available in software after 100 years? And to make the choice more realistic, let's assume that the algorithm must be sufficiently fast today (like md5 is).

The answer is that you don't want a hash, you want a solution that is ArchiSig or TR-ESOR (or something similar) compliant.

So what's the right algorithm to use instead of md5 if I just want a fast checksum that's widely supported?

BLAKE2b or BLAKE2bp should be a good choice for that. Or just CRC if you care only about unintentional changes.

SHA256

If SHA-2, do use SHA-512, since we are living in a 64 bit world.

SHA-512/256

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