At the risk of sounding OCD, on my 3rd guitar I;
1) Masked the purfling.
2) Stained.
3) Scraped the purfling.
4) Clear coated with a wipe on product twice.
...and here’s my contribution.
5) I scraped the purfling again. The wipe on clear coat may take up a little tint of colour, so the extra scrape really makes it look clean. By now the stain is locked in and doesn’t drag over the purfling anymore.