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We are even farther removed from the unfocused newspaper reviews
published in England between the turn of the 20th century and the eve
of World War II, at a time when newsprint was dirt-cheap and stylish
arts criticism was considered an ornament to the publications in which
it appeared. In those far-off days, it was taken for granted that the
critics of major papers would write in detail and at length about the
events they covered.Theirs was a serious business, and even those
reviewers who wore their learning lightly, like George Benard Shaw and
Ernest Newman, could be trusted to know what they were about. These
men believed in journalism as a calling, and were proud to be
published in the daily press. "So few anthors have brains enough or
literary gift enough to keep their own end up in journalism,' Newman
wrote, 'that I am tempted to define 'journalism' as 'a term of
contempt applied by writers who are not read to writers who are'.

1.What is the sentence "wore their learning lightly" supposed to mean?

2.What does the boldfaced word "they" refer to?

3.What does the sentence "could be trusted to know what they were about" mean?

What does the author intend to convey here in this sentence?

Wear one's learning lightly

This means to be knowledgeable but not boast about it or seek undue privilege from it. It means to behave in a modest and understated manner.

They knew what they were about

This is a slightly old-fashioned phrase, which in modern times is usually expressed

They knew what they were talking about

It means their remarks were knowledgeable and insightful.
In contrast, the phrase

He doesn't know what he is talking about

is applied to people who make statements that sound impressive, but are incorrect (in the sense of being confused rather than being incorrect).

To answer your question, "they" is the people described, such as Shaw and Newman.

What the writer is saying is that that generation of journalists was very knowledgeable and took their work seriously. Even those who were modest and did not make a big noise about their own high level of learning, actually did know a lot about the subject matter, and their opinions were well-reasoned.

In the closing quote, Newman is pointing out that journalism is a very demanding discipline, and many writers do not have the aptitude for it. Moreover he suggests that some writers who cannot achieve at this high level pretend that journalism is a lower form of literature, to enhance their own self-esteem. His final twist of the knife is to suggest that more people read a journalists' writing than a non-journalists'.