What about the USA bicentennial, or the St. Andrew's? Sure the USA national tartan would definitely be a neutral for those who live in the states, along with almost any national tartan (if you live in the respective country)?

The Black Watch does form the basis of many tartans, military and clan, but I have read of folks who have served in the military taking offense to those wearing it who have not served...so neutral, maybe...depends on who you ask. Pride of Scotland should be a safe neutral as well. If you can find your state or district tartan, that should be a perfectly acceptable medium as well.

that's about all I can add at this point.