Getting a 500 lumen LED light to put on my new 15-22. My question is ...Will the light have any effect on a red dot scope or should I buy a cross hair scope ?

should not have any effect if it is a good throw beam, pinpoint also. my lights on my tacticool AR's don't affect the eotech's, aimpoints, or the S&B or Weaver Superslams or the RMR's on any of them since the dot is not projected. a laser OTOH may not be able to be seen, but since the dot is internal there usually is no issue.

If the red dot or cross hairs can be seen during the day, then they can be seen while using a flashlight.

Most people mount them and never use them anyway.