は and を can be interchangeable when it is put after object, but there are some exceptions.
The most typical usage of を indicate the word is object. すしを食べません。 means 私はすしを食べません。 which can be translated as "I don't eat sushi."
And the most typical usage of は is to indicate the word is subject. 私はすしを食べません。 means I don't eat sushi.
は also can be used to indicate the word is object. But it sounds like there is an exception. So if you say 私はすしはたべません。, it doesn't simply means "I don't eat sushi", but it sounds like there are some food you can eat.
By the way, you also can say 私は寿司も食べません。, and it sounds like there are more similar example like sushi you don't eat.
Here are some examples:
As you can see, 1, 2, 5 are good because you eat 肉, but すし。, and these 2 objects are exceptions. Using "も" is wrong in these sentences because you are talking about two different foods you eat and don't. も sounds like there are more example, not exception. You could say like 4, sounds like you have 肉 and すし right front of you and you declared to eat 肉 but すし.
Here are some more example in case you eat both:
Using は is wrong in those sentences because you eat both 肉 and すし, there are no exceptions here. You should use "も" at least last sentence to indicate 肉 and すし are the same thing you can eat. You could say like 5 and 8, but it doesn't sounds like you are just talking about what kind of food you eat, but it sounds like you declared to eat sushi right now, and you eat 肉 later.
Why the meaning of the 5 and 8 have changed? That's because when you say "私はすしを食べます。", it is usually talking about what you usually do, but it also can describe what you are about to do, depending on the situation. And 5 and 8 are grammatically strange if you assume it is talking about what you usually do, but what you are about to do. That is what native speakers feel, but you don't have to concern too much about the idea of 5 and 8.
Note that も also can be used two examples that you DON'T do. 私は肉を食べませんが、すしも食べません。 私は肉も食べませんが、すしも食べません。
In a conclusion, I recommend you to use を right next to a object. But if you want to talk about two or more than two objects, you also should use も or は, depending on the situation. If the 2 objects are the same thing, you should use を or も at the first sentence, and you should use も at the second sentence.
If the 2 objects are the two different things you should use を or は at the first sentence, and you should use は at the second sentence.