Go for it. If BattleBots really is able to sponsor your team, then I agree that the "olive branch" aspect will be helpful. FIRST and BattleBots, although they approach the issue from VERY different perspectives, are both pursuing some common goals. And I would be surprised if any of the teams that truly practice gracious professionalism would give any team a lot of flack for the sponsorships they have gathered.
But your question brings up an interesting point. I have never seen it explicitly written down anywhere, but there seems to be a de facto policy in place that says teams don't seek sponsorships from tobacco companies, liquor companies, adult publications, used car salesmen, or the U.S. Congress
. I suspect that this may be defined at some level by the policies of the individual schools supporting the teams, but you never know. Are there sponsors from whom you would never accept support? Or from which FIRST should never accept support? Has your team ever discussed the "quality" or "corporate values" of the sponsors that you seek?
-dave