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

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