The conjunction that has a function. Sometimes it's redundant because when the that is missing, the meaning of sentence is still instantly clear. Therefore, the that is often optional.
Some people see the word "optional" and apply it dogmatically: that's the norm for most language users and rule followers.
Careful writers think about each instance and decide based on whether the sentence works better with or without the that.
In the sentence that you ask about, my feeling is that it reads better and is clearer with the that than without it, but that's just one man's opinion. I prefer to use the conjunction, but perhaps that's because I studied French, which has an equivalent structure that's almost always (I'm not sure whether it isn't dispensable in some cases) required. Other native English-speakers will have different opinions.
Both versions of the sentence are grammatical and acceptable and clear.