Hi,
I would think that if you were to plan around not spending much time near the boarder and get some miles on by starting early that you will be out of the hot spots quickly. Follow the basics of travel, don't ride at night, don't be flashy with wealth ect.
Your parents are correct in that they are having a problem in Mexico but keep in mind that it is a very large country and that there is way way more wonderful people in Mexico then bad. If you look at most of the effected, it is within the drug culture. An unfair comment to the innocent victims but tourists are not that often effected or targeted.
Do your homework and look at where the disturbances have been and do your best to get through those areas with expediency and follow some common sense rules of travel.
That's my 2 cents worth :-)
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