I walked this route in May 2014 starting in Seville and loved it!! The flowers, the green grasses, the flowers, fields of grains, the flowers, blue skies, the flowers, the beautiful landscapes, the flowers, the wonderful people, the flowers, stork filled nests...did I mention the flowers? It was a wonderful time to walk. Some hot days, mostly pleasant days, a few cool days. Spring/early summer followed me all the way northward. It was an amazing journey. You won't be disappointed.
Of course security is ever changing everywhere. I walked out of Seville with a woman looking for company because of the robberies that had happened and walked in at the end of the first day with she and another lovely lady we met along the way. We experienced no problems, but of course things can happen and I suppose things can change day to day. I understand that the people involved were later arrested. Like any travel one just needs to be aware of things going on around them. There will be people you can walk with if you feel concerned. I was contacted here on this forum by two women prior to departing home to walk out of Seville with them. One arrived in time and as mentioned we walked out together. The other arrived later than expected, but we met each other later and have subsequently stayed in touch and she was fine. I hope you enjoy your experience. It really is a special journey.