I would consider that something to worry about and investigate it further. You might want to check a plot_rank of the problematic variable for example.
Rhat diagnostic is basically a comparison of within and between chain variances. If all chains are sampling the same distribution (which is the case if the MCMC has converged), it will necessarily be close to 1 as within and between chain variances will be the same. If there are convergence issues, chains might have different variances as they aren’t (yet) sampling from the MCMC target distribution.
A deterministic transformation which is applied to all chains cannot make the different chains represent different distributions if they were originally all samples of the same distribution. What is possible is that the transformation in question is ill-conditioned and makes small differences much more noticeable. This you might be able to see with the extra investigation (i.e. a 1.03 on the original variables translates to 1.15, and a 1.02 to 1.08, something like that)