"I wish I didn't do" vs. "I wish I hadn't done"

Those are two separate sentences. There's no reason for the tenses in different sentences to agree. Consider:

Yesterday it was cold. Today it is warmer. Tomorrow it will be cold again.

So yes, you want hadn't:

Now I feel sick. I wish I hadn't eaten pork with cheese for dinner.

I believe you are asking about matching tenses.

Firstly, notice that both sentences are correct but they have different meanings.

1.

Now I feel sick. I wish I didn't eat pork with cheese for dinner.

This is an expression of regret for a commonly repeated action. You can replace it with:

Now I feel sick. I wish I didn't habitually eat pork with cheese for dinner.

2.

Now I feel sick. I wish I hadn't eaten pork with cheese for dinner.

This is a regret for a one-off action, we could say, e.g.

Now I feel sick. I wish I hadn't eaten pork with cheese for dinner last night.

Answer

Now we come to the matter of matching tenses. Let's look at the following:

*Now I feel sick. I wish that I hadn't eaten pork with cheese for dinner last night.*

Notice that I have inserted the implied "that".

There is no conflict of tense. The tense structure is -

a. now I feel sick - present tense of 'to feel'

b. now I wish (something) - present tense of 'to wish'

c. that I hadn't eaten - subordinate clause, past perfect

The statements are grammatically correct but would not be spoken by a native speaker. The sentence "Now I feel sick," dictates a certain kind of language logic from an English language perspective for the following sentence.

The ideas can best be expressed in English:

1) I feel sick now. I wish I didn't eat pork with cheese for dinner so often.

1) I feel sick now. I wish I hadn't eaten pork with cheese for dinner.

In my opinion you really need the phrase "so often." and number two is how most native English speakers would express this pork and cheese problem. Number two cannot take "so often" because of the present perfect.