Starting towards an answer...
The cells in the taste buds actually renew far more often RENEWAL OF CELLS WITHIN TASTE BUDS:
The life span of the average cell is about 250 ± 50 hours
So cells in the taste buds change much faster than the claimed change in taste.
However, there are known examples of tastes that change over the lifespan, e.g. the perception of sweetness (Sweetness intensity and pleasantness in children, adolescents, and adults.).
But "complete change every 7 years" is too simplistic.
Moreover, not every taste perception changes for everyone (Age modifies the genotype-phenotype relationship for the bitter receptor TAS2R38)
They looked at variations of a particular bitter reception, and found
the change in PROP bitter sensitivity which occurs over the lifespan (from bitter sensitive to less so) is more common in people with a particular haplotype combination, i.e., AVI/PAV heterozygotes.
Note that these people do not change their genes with age, but the perception of the bitter substance is markedly different. (AFAIK it is in general not clear whether the change comes from the signal from the taste buds or from the perceived quality, i.e. the processing of the signal in the brain - but I don't have literature on that.)
The AVI/AVI had a low bitter sensitivity throughout the studied age (3 groups around 7, 15 and 34 years), and the PAV/PAV maintained high sensitivity.
This paper has whole sections on how taste likes and dislikes develop. Particularly dislikes can develop very fast, and also erraneously (e.g. childen can learn to dislike a food if they fall ill soon after eating it - also if the illness was completely unrelated to the food). They also cite this other paper saying that
Some research suggests that children need to taste a new food at least ten times before they change their preference (Wardle et al, 2003a), especially if its initial palatability is low. Mothers typically cease to offer foods that have been rejected on three or more occasions (Carruth et al, 2004) and as a result the necessary level of exposure required to create acceptance might not be reached.
So if those 10 exposures take 6 months, there you are...
About carrots: Here's a PhD thesis about bitter taste in carrots (in German). This leaflet about the project said that rather freuently intense bitter taste in carrot-based baby food leads to reclamations, and the project identified some substances but concludes that still not all precursors are known, so it is still difficult to measure the potential of the carrots for developing bitter taste.