Is it safe to use stain and polyurethane on a wooden trivet
Oil-based polyurethane is fairly resistant to heat (slightly more so than water-based), and it would seal well, allowing for easier cleaning and care. If you're not a terrible cook or one inclined toward flaming dishes, it should last well. 


  For trivets, the enemies are heat and food or water spills. Years ago, I made some trivets for the magazine and finished them with a 50/50 mix of oil-based polyurethane and mineral spirits. Its thinner consistency allowed the finish to flow down into the nooks and crannies well (my trivets had some intricate cutouts, as you can see in the photo below). Then, the excess was easy to wipe off. It soaked in and dried quickly, and I applied several coats. Over the years, we’ve continued to use this very trivet regularly, and the finish has held up well to all sorts of hot pots and cookie sheets. I recommend it.


More info