When gluing wood, there is always glue that squeezes out along the join. This tends to penetrate and mark the wood and shows up when the wood is stained or varnished.
To prevent this, use masking tape along the edges being glued. When the glue is touch dry, peel off the masking tape and use a scraper or putty knife to remove the remaining bead.
Voila! No wood staining!