Typically, people use the present tense, the future tense ("will"), or the present continuous ("be doing") in the clause following the verb "hope" in the present tense. (Reference here.) However a few examples use "would" in the clause instead:
I hope people would say in 20 years that Gwinnett County is a place where parents are interested and involved in the education of their children .
I hope things would not get that far.
This is his first book of poetry and he hopes it would perhaps influence and help others.
Whatever the editor replies, one hopes it would be in the form of a good rejoinder that one can later use for amusement.
(All above examples from Linggle.)
When is the use of "would" following "hope" in the present tense correct? How is the meaning different from a verb in the present or future tense?