I'm using a professional at home teeth whitening system (boutique whitening), must I adhere to a strict 'white diet'?

Hello Sara941
Thank you for your question and it is important as it is often the reason people do not end up whitening their teeth for as long as there would like or get the results they would like to achieve. 
I will start by saying that I have been involved in literally hundreds of whitening treatments over the last ten years and the vast majority have lead to happy clients and successful conclusions.
A few people struggled with the white diet as you have described and either could not find a point in their life where they could fit the whitening 'period' in or had staining foods and were not completely happy with the results.
The Gold Standard is to avoid any staining foods (anything that could stain a white shirt) whilst you are whitening your teeth. This is because the food stains can re-enter the tooth, slightly reversing the process of stain removal that you are trying to accomplish. 
Over the years dentists have suggested that you can have staining foods, a set amount of time after the whitening gel has been removed from your mouth. This can be 1 hour or 2 hours. This allows your teeth to re-stabilise and reduce the darkening effect of the food stains. 
If you stick to this (easier) protocol then you can have coffee but you need to remember the following:
The overall whitening time taken will be longer - you will not get the same result in two weeks as the staining foods are very slightly pushing the reversing the processYou will also need more whitening gel (which you will have to pay for)As the time taken is longer you may still overall get frustrated with the process and stop whitening early.If your teeth are particularly dark to start with the rate of progress may be so slow that it feels like nothing is changing. 

I expect that the dental nurse would have to pay less for each tube of whitening gel which would make this a less difficult decision for them. I would always suggest that you try to hold out as much as you can for the maximum benefit, but do not beat yourself up if you have too have a coffee. Just leave a 2 hour gap, during which time you can still have your white foods. 
Good luck and Kind regards

Thomas  Dey BDS, MSc