
they or a reader?

A reader

IF YOU LIKE IT I CAN GIVE IT TO YOU

why? keep it.

if it's a reader, why is it "they"?
An astute reader should be willing to weigh everything **they** read...

Read up 'singular they' on Wiki, it seems to be quite a topic of debate around.

thank you, Ooneykcall

As @sundown has pointed out, if the desire is to keep "they” gender-neutral, one way the sentence can be fixed without violating the norms of English grammar is to change the main subject to the plural:
Astute readers should be willing to weigh everything they read, including anonymous sources.
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