Something that's tasteless is either very bland, like a plain baked potato with no seasoning, or it's tacky and inappropriate, like the tasteless jokes your uncle likes to tell at Thanksgiving.
If your tuna casserole is tasteless, you should add some salt and pepper. If your relative is tasteless, that's a trickier problem to solve. In the latter case, tasteless means "lacking in judgment" or "offensive." So a joke that hurts someone's feelings is tasteless, and wearing a dress made out of rubbish you found in the recycling bin to your cousin's wedding would also be tasteless — unless the wedding's theme is "Reduce, Reuse, Recycle."