Can you list the reasons that you're thinking of not storing data on Github? I would assume that you have a (paid) user or organization account and keep the repo private, unless it was for a published paper.

I was thinking more along the lines of data that you'd want to graph or preset for analysis, as in a notebook or a paper. I would (hopefully) assume that your simulation data would be generated and used in such a way that it wouldn't need to be stored permanently. At least, when I was doing simulation based analysis, I wasn't necessarily concerned about any individual run, but rather a combination of a bunch of simulations (all of which were ephemeral).