Learn Hardcore Russian: Я против таких изменений в расписании. - I am against such changes in the schedule.

этих изменений = “these changes” (points to specific, known changes)
таких изменений = “such changes” (comments on the kind or nature of the changes, often with a negative tone)

Why is изменений in the plural genitive?

The noun изменение means “change.” Here the speaker refers to multiple changes, so the plural form is used.
After против, you need the genitive plural. The genitive plural of изменение is изменений.

What case is расписании in, and why do we say в расписании?

The noun расписание (“schedule”) is in the prepositional case after the preposition в, which here means “in.” The prepositional singular of расписание is расписании.

в расписании = “in the schedule”

Can we replace в расписании with something else to mean the same thing?

Yes. You can use synonyms for “schedule” or “timetable,” but the noun must still be in the prepositional case after в:

в графике (in the timetable) → Я против таких изменений в графике.
в плане (in the plan) → Я против таких изменений в плане.

Is я (I) necessary here? Can it be omitted?

In Russian, the subject pronoun я can often be dropped because the verb form implies the subject.

Против таких изменений в расписании. is grammatically acceptable in a clear context.
Including я adds emphasis or clarity: Я против таких изменений в расписании.

Could we say я не согласен с такими изменениями instead? What’s the difference?

Yes, you can, but there’s a subtle difference:

я против
- genitive is more direct/strong (“I’m against…”).
я не согласен с
- instrumental is milder (“I don’t agree with…”).
  Grammar difference:
  • против → genitive: против изменений
  • с (with) → instrumental: с изменениями