The horizon problem refers to the former mystery of why the universe is homogeneous and isotropic despite distant regions of space failing to be causally connected. Science has provided an explanation.
 Against rationalists
When confronted with the starlight problem, Young Earth Creationists occasionally counter that the big bang theory has a "starlight problem" of its own. Leaving aside the fact that this argument fails to address the problems with the YEC model, this criticism has been refuted.
The problem with the big bang that the creationists refer to is known in scientific circles as the horizon problem, which states that the universe is homogeneous and highly isotropic (it's largely the same in every direction we look) despite insufficient time for regions far away from each other to "communicate" and become roughly the same in temperature, density, and other properties. However, an explanation consistent with these and other observations has existed since the early 1980s.
 Argument refuted
The explanation, known as inflation, was proposed by Alan Guth and holds that the universe underwent a brief period of rapid accelerated expansion very early in its history. Inflation accounts for the observed homogeneity and isotropy of the universe, as well as the flat geometry of the universe. Furthermore, inflation predicts very small but observable differences in temperature of the cosmic microwave background radiation, which have since been confirmed by satellite-based measurements.
The inflationary big bang theory continues to be, overwhelmingly, the best scientific explanation for the beginning of the universe.