Q:

Using both “one’s” and “their” to refer to the same entity

Consider this example:

Sustainability management in large organisations is an important activity that helps to achieve one’s business goals while at the same time reducing their environmental impact and improving benefits to wider society." 

Does it make sense to use both one’s and their to refer to organisations in the quoted sentence above?  

A:

Whether it makes the best possible sense, one cannot comment upon with certainty, but it is neither uncommon nor new to arrange one’s pronouns in this way. 
In this instance, you cannot help but wonder whether using two different pronouns necessarily implies two different referents, and so you reread and reassign trying to make some pair of choices so it reads sensibly.   You waste a bad bit of time this way, and you aren’t ever quite sure your guesses are right. 
A careful writer might well wish to make both their pronoun references look the same, for if they were to do so, there would be little cause for complaint.   
Well, except that peppering a sentence with too many instances of one and one’s and oneself gets a bit heavy-handed, so a bit of relief from they and theirs and themselves (and with courage, even themself) can break that stuffiness up.   
But do as thou wilt. 

Edit
There can be no question whether the sentence is grammatical: it is.   That doesn’t mean it’s sensible.   Colorless green dreams resting furiously is grammatical, too — and nonsense. 
The real problem is what we have no idea what the devil the cited passage actually means.   Because that question arises, we know that it’s its style, not its grammar, wherein the problem lies. 
Peter Shor points out that the intended antecedent of their might be business goals, not organisations nor one.  If he is correct, then this makes it the business goals’ environmental impact which are under discussion here.  Maybe. 
This may well be the writer’s intent, but if so, she should have made this clear instead of making her readers puzzle over what goes where.  She should throw the entire miserable sentence down the garbage disposal.  This writer needs to start from scratch, carving up her long and confusing sentence into several shorter and clearer ones — and preferably ones where you don’t feel like she’s playing all three of Buzzword Bingo®, Pronomial Twister®, and Nominalization Balderdash® at the same time.  Nor any at all, really.  
That’s all I have to say, because — doubt it though ye may — I’ve just run out of new personal pronouns to use in new paragraphs.  

A:

I would say No.  In the sentence

Sustainability management in large organisations is an important activity that helps to achieve one’s business goals while at the same time reducing their environmental impact and improving benefits to wider society. 

it's not clear what their is referring to.  Is it the business goals, or the large organisations?  
Who is one?  Generally it's a non-specific person, or perhaps — royalty are prone to this — "me".  It's a singular pronoun.  It does not refer to the large organisations! 
The word one's should be their.  And you can probably remove the second their because "benefits" are not attributed to anything in particular either.  The second their could remain, but might be more awkward than removing it. 

Sustainability management in large organisations is an important activity that helps to achieve their business goals while at the same time reducing environmental impact and improving benefits to wider society.