I'm not sure I fully understand your question and statement. Do you mean sport becomes another issue when two countries have political differences, or it causes more issues?
Either way, I think sport can be an olive branch between two countries. In the early 70s, South Africa's apartheid policy was greeted with condemnation in Australia when their national Rugby Union team toured the country, resulting in riots at every game. The result being the exclusion of South Africa from World Cups and most other sporting events, including the Olympic games, until that policy was abandoned when Nelson Mandela and his government was elected to power. It was then sport that helped to bring the country back into favour. I consider sports more of a commonality than an obstacle.