Is it possibly wrong to be written like this?
If there is to be toleration in the world, one of the things taught in schools must be the habit of weighing evidence, and the practice of not giving full consent to propositions which there is no reason to believe true. For example, the art of reading newspapers should be taught. The schoolmaster should select some incident which happened a good many years ago, and roused political passions in its day.

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one of the things taught in schools must be the habit of weighing evidence, and the practice of not giving full consent to propositions which there is no reason to believe true.

In this sentence, I think the part ", and the practice of" can be taken away.

"the habit of weighing evidence and not giving full consent"
Is it possibly wrong to be written like this?
I think the two sentences covey the same meaning anyway.

Please help me!
Thanks!!

Question

Is it possibly wrong to be written like this?
If there is to be toleration in the world, one of the things taught in schools must be the habit of weighing evidence, and the practice of not giving full consent to propositions which there is no reason to believe true. For example, the art of reading newspapers should be taught. The schoolmaster should select some incident which happened a good many years ago, and roused political passions in its day.

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one of the things taught in schools must be the habit of weighing evidence, and the practice of not giving full consent to propositions which there is no reason to believe true.

In this sentence, I think the part ", and the practice of" can be taken away.

"the habit of weighing evidence and not giving full consent"
Is it possibly wrong to be written like this?
I think the two sentences covey the same meaning anyway.

Please help me!
Thanks!!

Answer

Your proposed change can work but it violates the principle of parallel construction.  
http://grammar.ccc.commnet.edu/grammar/parallelism.htm

"This principle, that of parallel construction, requires that expressions of similar content and function should be outwardly similar. The likeness of form enables the reader to recognize more readily the likeness of content and function."

So the sentence can be broken down as follows:

One of the things taught in schools must be

a) the habit of weighing evidence, and 
b) the practice of not giving full consent to propositions which there is no reason to believe true.

both (a) and (b) have the structure "the x of verb'ing y"

In  (a), x="the habit" verb="weighing" y="evidence"
In (b), x="the practice" verb="not giving" y="consent to ...."

The original sentence uses parallel construction.  Your proposed modification does not.