Is it acceptable that I plot a time-series figure with years increasing from right to left? I have a plot like this in my paper, but one of the co-authors says The x-axis is backward. I think as long as keeping all figures in the same style, it is ok. But I am not sure if there is really such a rule that years should increase from left to right? My field is environmental science.
I think readers will be strongly expecting that time increases from left to right in a graph.  It's probably not a "rule" that you'll find written down anywhere, but it's certainly the overwhelmingly common practice. Having time go from right to left will very likely confuse your readers, and I don't think it should be done unless there is a very strong reason for it.