When two people make a voluntary trade, both do this because they gain from this trade. As an effect, value is created.
Every trade creates value.

BitcoinCash registers one part, the money side. We mostly assume the other side of the trade happens too.

But what if it doesn’t?
And why would we care?

These questions go towards what gives money value, assuming we don’t have some government fiat saying it has value, then what makes a chain like BCH worth some specific amount of dollars? Why would that number go up? Or down?

The simple answer to that is that when a trade is made and money is involved, then that money also becomes more valuable. Not in the literal sense, as money doesn’t get created out of thin air.
But the value in the world went up due to the value created by the trade, and the money that represents that is unchanged, same number of coins representing that bigger amount of value.

When a carpenter takes plain wood and makes some shelves which hey then sells, he created real value. A measurable value, even.
Selling his shelves for BCH makes the chain gain value too. And this is how money becomes valuable. By being used for value-creating trades. Which is most trades.

This answers the “why would we care?” question.
We care about transactions on our chain representing real trades because those transactions make the actual value of the chain go up.

So, what kind of transactions do not make the chain-value go up?
Good example is the memo website; it is a twitter competitor and instead of innovating, they just piggy-back on BCH and drop the text messages on the chain. No value is created that resulted in those transactions. Its a person paying themselves and adding some extra data to be stored on the blockchain.

It is worth noting that pure trades are the simplest way to create value. They are not the only ones and there are other ways to create value.
Many cash-tokens based ideas are not exactly trades. Some of the coolest ideas for cash tokens are things like company voting or maybe paying dividends.

The value is still created, but more indirectly. Operating a company that creates sales (in BCH) is obviously great. Operating such a company takes more than just sales, paying dividends is a good example. Having more of the company structure on the same chain creates a lot more value as well and will very likely create more sales which are to be in BCH.
Such transactions are probably still value creation. Just a little more long-term style.

I’m looping around and going back to the question; why would we care?

Do we care if someone puts 32MB of transactions which have no economic activity on Bitcoin Cash? And if no, at what amount would we start caring?

The answer is about balance. Let me explain with a tree-of-life:

Everyday trades are the trunk of our tree, the more there are the bigger and sturdier the tree-trunk and thus our entire tree. On a big tree there is no problem with some side-branches sticking out quite far.
We just have to keep the balance, should the side-branch get bigger than the trunk, the whole thing will collapse.

Bitcoin Cash is balancing this quite well, so far.
Understanding why this is so, is crucial to keep it working well.