In journalism, never write e.g.: eg = exempli gratia But who knows the old Latin expression exempli gratia? Did you know? I didn't. I had to look it up. Exempli gratia is Latin for the English expression "for example". Stick to English rather than Latin. If you mean "for example", then write in English and write in full: for example.
This is part of a bigger rule that runs right through good journalism: write in plain English, and never send your reader to a dictionary of dead languages. Latin tags like eg, ie, etc, nb and viz belong in old legal documents and dusty textbooks, not in a newspaper that ordinary people read over breakfast.
The danger with "eg" is not only that some readers will not know it. It is that even readers who think they know it often muddle it up with "ie", which means something completely different. (See my separate note on ie versus eg.) When a single tiny abbreviation can be misread, the safe and friendly choice is to spell out what you mean.
So when you want to give an example, write "for example" or "such as" or "like". They are warmer, clearer and impossible to misunderstand. "Many native birds, such as the magpie and the kookaburra, are protected." Nobody has to pause, nobody has to guess.
Plain words cost you nothing and gain you everything. Leave the Latin to the lawyers.