Hold Up

I would not use "example" in the first sentence, but I would in the second.

This use of "hold up" means "to call attention to" or "to single out."
The man is not being used as an example. Rather, his heroism is being pointed out. The focus is on the man.
The project, however, is being used as a example. The focus is on governmental waste.

I hope this helps.

"The earthquake is held up as a major natural disaster."
"The earthquake is held up as an example of major natural disaster."

Which one should I use?

Again, I would use "example."

So, "an example of" is necessary for non-humans, but not so for humans?

The humanity is irrelevant. The question is, what is the subject?

For example, my dictionary has "his writing was held up to ridicule." (The subject is "his writing" not "things which are ridiculous.")
If you said "His writing was held up as an example of bad writing," the subject has changed. Now the topic is "bad writing" (of which his writing is an example).

Do y

So,

"He is often held up as a hero."
should be read in the spirit of:

"His writing was held up to ridicule."
?

Yes. In both cases, the focus is on the person or the works rather than on how these are examples of something bigger.

Thank you Doctor D!