1. It also means developing new business relationships with our customers and suppliers that are a radical departure from traditional approaches. The sentence is poorly constructed. It should be restructured: 1. It also means developing new business relationships, that are a radical departure from traditional approaches, with our customers and suppliers.

The sentence is okay because in attributive clauses if the noun being modified was a person we would use 'who'. Here the noun being modified is 'new business relationships with our customers'. (These are the specific relationships we want to develop) If you move the clause you change the meaning and the noun being modified becomes only 'new business relationships'. So obviously it depends on what you want to say.

Agree with JackquiD. In writing, "that" will only modify a thing and "who" will only modify a person. Just remember that in conversation people will often use "that" to modify a person too. Usually an attributive clause modifies the noun that comes directly before it. In this sentence there is a prepositoinal phrase ("with our customers and suppliers") and so it is a bit confusing. Honestly, the rule here is you have to figure it out based on the context. It doesn't really make sense to say that "customers and suppliers" are "a radical departure," therefore the clause is modifying "new business relationships."