Why Krishna engaged in Rasa Lila with married Gopis? 

SRILA PRABHUPADA SAYS:

“The Isopanisad states that the Lord is "the greatest of all, unembodied,  omniscient, beyond reproach, without veins, pure and uncontaminated." 

No sin can pollute Krsna. Sometimes less intelligent persons criticize Krsna: "Why did Krsna engage in the rasa dance, enjoying with other men's wives in the middle of the night?" 

Krsna is God. He can do whatever He likes. Your laws cannot restrict Krsna. For you there are so many restrictive laws, but for Krsna there is no restrictive law. He can surpass all regulations”. 

Pariksit Maharaja asked Sukadeva Gosvami: 

"Krsna came to establish the principles of morality and religion. Then why did He enjoy the company of so many young girls who were the wives of others? This seems to be very sinful." 

Sukadeva Gosvami answered: “Krsna cannot be contaminated by sin; Rather, whoever comes in contact with Krsna, even with a contaminated mind, becomes purified. The sun is a good analogy: the sun cannot be contaminated;  Rather, if something contaminated is placed in the sunshine, it becomes purified. Similarly, you may approach Krsna with any material desire and you will become purified. 

Of course, the gopis' feelings toward Krsna are not at all material. Still, as young girls they were captivated by His beauty. They approached Krsna with the desire to have Him as their paramour. But actually, they became purified. 

Even demons can become purified by coming in contact with Krsna. The demon Kamsa, for example, thought of Krsna as his enemy. But he was also Krsna conscious, always thinking, "Oh, how will I find Krsna? I will kill Him." 

That was his demoniac mentality. But he also became purified. He got salvation. 

The conclusion is that if we can somehow or other develop our Krsna consciousness, we will immediately become purified of all sinful desires. Krsna gives this chance to everyone”.