Omissibility of "to be" before Noun or Adjective [duplicate]

The verb BE can sometimes be omitted in English without losing grammaticality or changing meaning. (guinlist. press)

So, whenever we will agree here that be is omissible, it would mean that neither grammaticality nor meaning will be changed. The omissibility of be between an object and its complement is no easy matter, and it depends on the choice of verbs.

Grammar errors are likely in this area because many verbs whose object can be followed by a complement-like noun or adjective either require mention of to be or forbid it – they do not allow a choice about it.

As for think, it belongs to the category of those verbs that can, "at least sometimes", omit to be before an object complement (whether it is an adjective or noun):

• Plato considered the world (to be) a copy of reality.
  

The object here is the world, and the object complement is a copy of reality. Other verbs usable at least sometimes in the same way include many that can have a “descriptive”, “role” or “belief” complement, such as APPOINT, BELIEVE, DECLARE, ELECT, FIND, JUDGE and THINK.

So whether to be can or cannot be omitted is not dictated by the fact that it is followed or not by a noun object complement, but by the verb choice.

But I find your example with believe particular. I don't think She believed him a teacher is common, in fact Gngram finds no instance and I think this is because the object complement (a teacher) does not really express opinion. GNgram did find such instances:

She believed him a monster.

Here opinion is much stronger. Consider seems to be much more prone to omiss to be:

CONCLUSION: It would be easy to have a set rule and just follow it, but this is one more proof that English does not work this way. The omissibility of to be is dictated by verb choice, by the element of opinion, but also by the behaviour of each verb in part. Also, I think it would be fair to say that the omission of to be before adjectives is much more common than before nouns, but the latter can and does sometimes occur within the boundaries of grammaticality.