Majority filter would work
But if you want to be selective:
For example, in your image, there are several dual zones where 2 blue pixels adjoin. If you want to replace both of those as well then you can do a combination of
Regiongroup to identify the small areas it will create individual zones from the input data like a sequential list
SetNull to mask the small areas You can also use Con with SetNull but doing the query on the count field
Nibble to remove the small zones
In that way you can remove zones of 1, 2, 3,... x cells even if your maps consists of 2 classes but dozens+ of discrete zones. Remember, raster data are like multipart data in vector world, you need to convert the multipart representation to singlepart in order to process 'fiddly bits'