1. It is strange that he didn't come... 2. It is not primarily a brand that we ...

[wotcha]

1. It is strange that he didn't come back.

2. It is not primarily a brand that we are choosing.

Which 'that' can be omitted between the two sentences?

 

[BobK]

Depends on register. You can drop the that in 2, but in 1 you can only drop in speech - when intonation says 'Here comes a subordinate clause'.

b

 

[MikeNewYork]

I consider "that" optional in both sentences. It is normally only mandatory when it is the subject of the relative clause. That said, it would be commonly used in #1.