[edited based on helpful feedback in the comments]
It bothers me immensely when people do this. The argument against it is simple: the standard deviation is typically shown to convey information about data distribution (and standard error for a parameter). It achieves this goal well in some situations but not others. If the standard deviation/error implies that negative values are reasonable when you know they are not, it is not helping you communicate accurately. Bimodal distributions are another situation in which mean ± SD/SE is likely to mislead.
So what else can you do? If you're interested in the data distribution, just show the full distributions using density plots, violin plots, histograms, or their alternatives. If you're interested in the uncertainty of a parameter, you could show confidence intervals or the posterior distribution. Unlike standard deviation or standard error, these options can be asymmetric and will communicate the data distribution or uncertainty more accurately.
If you must use a numerical summary for a data distribution without referring to a graph, you could use quartiles instead of mean ± SD.