This leads to several different sentences. Each of them is grammatically correct, but they do not mean the same thing.
I'm afraid that she will be mad at me if I cancel the plan, ....
This is the most basic and straight-forward version. The speaker fears anger on the part of the unspecified female person.
I'm afraid that she may be mad at me if I cancel the plan, ....
Here the speaker thinks that such anger is possible, but is quite unsure if it will occur or not.
I'm afraid that she might be mad at me if I cancel the plan, ....
This is intermediate between the first two. The speaker is still unsure about the anger, but thinks it more probable than in the "may" case.
I'm afraid that she would be mad at me if I cancel the plan, ....
In this version, the speaker is reasonably confident that she will be angry if the speaker cancels. This version is placed in an unreal future, using the subjunctive mood to emphasize that the speaker will not cancel, and so the anger will never actually happen. The meaning is much the same as the version using "will", but the emphasis is on what the speaker will do, or actually not do.
I'm afraid that she should be mad at me if I cancel the plan, ....
This was once a common if somewhat formal usage, with a meaning somewhere between the "will" and 'might" forms above. That usage of should is now uncommon, and is becoming obsolete. Learners should avoid trying to use it. However, "should" can also mean "ought to" or "is expected to". In this case the meaning would be "She ought to be made at me if i cancel" suggesting that some sort of social rule requires such anger. This is unlikely, unless the setting is a rather different society from current mainstream US or UK society. (I could imagine such a statement in a work of SF in a setting with very different social rules.) However, other uses of "should" that are somewhat similar in form are plausible:
- She should decline to accept such an unfavorable offer.
- She should be angry at such an insulting suggestion.
In both examples the speaker is not predicting what she will do, but rather indicating what someone thinks it proper that she do. It is not clear if that someone is the speaker, or society at large, or who it might be.