To overlook, to ignore, to disregard, to neglect should be appropriate to use in place of this idiom. The meaning of the idiom is to ignore deliberately, to pretend not to notice. (See the idiom's entries in WordReference.com and CollinsDictionary.com.) In fact there are many synonyms for this.
According to Phrases.org, the origin of the idiom goes like this: Admiral Horatio Nelson is supposed to have said this when wilfully disobeying a signal to withdraw during a naval engagement during the battle of Copenhagen in 1801, when the Admiral Sir Hyde Parker sent a signal (by use of flags) for Nelson to disengage. Nelson was convinced he could win if he persisted and that's when he said to have 'turned a blind eye' on the flag signals. Chapter VII of the biography The Life of Horatio Lord Nelson by Robert Southey claims the actual words of Nelson to Captain Thomas Foley were:
"... You know, Foley," turning to the captain, "I have only one eye,—I have a
right to be blind sometimes:" and then putting the glass to his blind eye, in
that mood of mind which sports with bitterness, he exclaimed, "I really do not see the signal!"
And thus the idiom "to turn a blind eye" on something/someone.
Thus, using ignore, dismiss, disregard, overlook, pretend not to see should be fine depending on the exact requirement of the sentence. For example:
Only parents could overlook that kind of behavior.
Only parents could turn a blind eye on such behavior.
Teachers overlooked the bad handwriting in cases where students were
able to secure only passing marks.
Teachers turned a blind eye to the handwriting in cases where students
were able to secure only passing marks.
The corrupt inspector agreed to pretend not to see the safety
The corrupt inspector agreed to turn a blind eye to the safety violations.
The Management ignores the bullying at the workplace.
The Management turns a blind eye on the bullying at the workplace.