When working with small parts, I often find it easier to stain them before assembly. I get better results. The problem I run into is when I forget to properly mask off a glue joint first, and the glue won’t stick. Is there a good solution?
Pre-finishing, including adding color, is a great way to improve the quality of your work. But as you have found out, it also has its risks. If you are asking what to do after you have applied an oil-based pigment stain to parts that then must be glued together, the only answer is to sand, scrape or in some other way remove the oil film from the affected area.
An option that some woodworkers are unaware of is using dye rather than pigment stain in delicate pre-finishing work as you have described.
The operative difference between dye and pigment stain is twofold. First, the molecules of the dye are so small that they don’t create a layer of “stuff” — as does the ground-up earth in pigment stain. Also, when the dye is suspended in water or alcohol, the liquid evaporates away leaving the wood without a layer of oil on top.
The benefit is, you can glue together wood that has been dyed just the same as if it had no coloring on it at all.If you also want top re-finish using your top coat, you still need to mask off the joint or you are back to the same problem. Good luck and try some dye!