The expression “to strain at a gnat and swallow a camel” means: To make a fuss over trifles but accept great faults without complaint.
This, as are many others, is a Biblical expression.
It is found in Matthew xxiii, 24-26: “Ye blind guides, which strain at a gnat and swallow a camel. Woe unto you, scribes and Pharisees, hypocrites! for ye make clean the outside of the cup and of the platter, but within they are full of extortion and excess. Thou blind Pharisee, cleanse first that which is within the cup and platter, that the outside of them may be clean also.”
But the translators of the King James Bible of 1611 were already familiar with this figure of speech.
It had appeared in Lectures upon Jonas by Bishop John King, first printed in 1594, reprinted in 1599, in which the bishop himself said, “They have verified the olde proverbe in strayning at gnats and swallowing downe camells.”