Barley and Wheat question

Sorry if this is a stupid question. 

First the Barley questions.  Our neighbor and I have been coordinating our gardens because of cross pollination.  Somehow we missed that we both had Barley.  It's self-pollinated, but they say there is still a 10% chance of cross pollination.  Between us is the state forest and heavily wooded land, slightly under 1 mile apart as the crow flies.  Is that enough space of should one of us skip this year?  Keeping the seeds true is very important.

Second, do red and white wheat cross pollinate?  If so and you had to plant just one, which would it be?

Thanks for any input!!!

According to this website, http://www.topcropmanager.com/content/view/3850/38/ barley, wheat, and oats all self-polinate, and therefore different types of these plants can be grown in relative proximity without risk of cross-polination. Rye, apparently, is different. If this information is accurate, and I have every reason to suspect it is, then you need not worry about mischeif from your neighbor's barley.

Hope this was helpful, if not altogether timely.

also something I read last month about rye was that the rye that is planted for grass ..mown grass..is not the same type of plant as the rye planted for food, so there shouldn't be any worry about crossing there either...but this isn't a prof opinion