If you're lucky, you might start with reasonable freedoms when you first experiment with creative techniques at work, even if you're in a traditionally analytical sector.
But it doesn't usually last long. For all sorts of reasons, you're likely to be challenged about the value of your new approach, and you'll need to consider how to tackle that.
The obvious responses are supported by:
Evidence - Demonstrate where the approach has generated something of business value rather than purely of academic interest. Ideally this should have occured where other more sequential methods had failed. For maximum impact the exercise should have been conducted like a scientific experiment, with an initial hypothesis, controlled variables, and measured outputs.
Opinion - Draw on support from steady, well-regarded people who have always believed in the value of creative thinking, and more importantly from those who have recently become converts.
Direct action - Cajole, wheedle or reward your cynic for getting directly involved in creative brainstorming (though you might improve your chances if you call it something else!) This is one area where your cynics' pre-dispositions can help: Invite them to critically analyse the effectiveness of other competing techniques, and also to recognise the merits of experimentation.
Analysis - Consider what might be behind the cynicism. Is it that the opposition results from previous experience (find out what happened), too little time (take some load away), jealousy (be inclusive) or just received opinion (arrange for alternative opinions to be aired).
Creativity - Use your preferred techniques for creative thinking to arrive at your own alternative responses, by focusing on the specifics of your situation.
If all else fails ... ignore the cynics, and try to take comfort in knowing something they don't!