You may want to take a look at the Home Improvement Help Page. To summarize what you can read there:
- It is considered on-topic to ask questions regarding the repair and maintenance of major appliances.
- Questions regarding the operation of major appliances are considered off-topic.
So your question generally seems to apply to the second item above. In some cases there is a gray area between repair/maintenance and usage/application. My guess is that your refrigerator is just not broken or in need of maintenance/repair. Sometimes you have to make a choice to post and let the community decide via their votes.
Getting to your actual question....it is often not recommended to plug a refrigerator into a GFCI protected circuit due to the fact that the compressor is a "motor" load which can cause problems with GFCI. That said I am sure that there are conflicts between that recommendation and the up to date electrical codes regarding various electrical receptacles in your kitchen.
It is possible that I did not fully comprehend your situation and that more discussion is required.