First the good news, soccer fans in KC will not have to decide between Sporting and FCKC being at home on the same day. Unless the Blues host the NWSL final on August 31st, the two teams will not play at home on the same day. But there will be points when fans may have to choose between watching a team live vs watching on TV.
Six times over the course of the season, the two teams play on the same day. The first of the conflicts comes on April 20th when Sporting KC are in LA for a 9:30pm start while FCKC is at home to take on the Boston Breakers at 7:35pm. The second is in July, when FC Kansas City kicks off at 6:30pm in Washington while Sporting KC is at home against Vancouver, kicking off at 8pm. It happens again 4 days later on the 7th when Sporting KC kicks off at 2pm in Chicago and the Blues take on Western New York at home at 3:10pm. It happens for a 3rd time in July on the 20th, when KC takes on Seattle at home at 7:35pm while Sporting KC kicks off at 9pm in Salt Lake. It happens two more times in August. On the 10th FCKC kickoff in Boston at 5pm while Sporting KC kick off at home at 7:30pm against the Boston area's men's team, New England. The final regular season conflict is on the 18th, when FCKC kick off at 3:10 in their home finale against Chicago. Later that night at 10pm Sporting KC kick off against San Jose.
There are also three weekends where you can make it a soccer weekend in KC with both teams being at home on the same weekend. The first example of that is FC Kansas playing at home vs Seattle on Friday April 26th and then Sporting is at home on Saturday the 27th. Maybe the best weekend of the year is Memorial Day weekend, when FC Kansas City is home on Saturday against SKy Blue FC and Sporting KC is home on Sunday the 26th against Houston. It again takes place at the end of June with Sporting KC at home on the 29th against Columbus and FC Kansas City on Sunday vs Portland.
Here's a look at the way the schedule as a whole breaks down between Sporting KC and FCKC from April through August, the length of FCKC's season. (Click on each one for a bigger picture.)