Miriam and Aaron were griping about the position that Moses held and comparing themselves, as they said, "Hath the LORD indeed spoken only by Moses? hath he not spoken also by us? And the LORD heard [it]. - (Num 12:2 KJV)
Compare that to what was spoken of in Jude: the Gainsaying of Core -
"And they gathered themselves together against Moses and against Aaron, and said unto them, [Ye take] too much upon you, seeing all the congregation [are] holy, every one of them, and the LORD [is] among them: wherefore then lift ye up yourselves above the congregation of the LORD?" - (Num 16:3 KJV)
Both were challenges to the authority of Moses and both were dealt with, shall we say, "expeditiously".
The Lord did not smite Aaron but Aaron had immediately begun the job of intercession, for Miriam. Moses also sought the Lord on her behalf.
2Tim 2:16 admonishes us to "shun vain and profane babblings, for they shall increase unto more ungodliness." Proverbs 6:34 says, "Jealousy is the rage of a man". This refers to mankind, not just men -- we don't think of this as sexist, but it does point to the sin of all three, Miriam, Aaron and Korah.
As far as the allegation that God behaved in a sexist manner because Miriam was struck with leprosy and Aaron wasn't, Korah was sawllowed by the earth! "And the earth opened her mouth, and swallowed them up, and their houses, and all the men that [appertained] unto Korah, and all [their] goods. They, and all that [appertained] to them, went down alive into the pit, and the earth closed upon them: and they perished from among the congregation. And all Israel that [were] round about them fled at the cry of them: for they said, Lest the earth swallow us up [also]. And there came out a fire from the LORD, and consumed the two hundred and fifty men that offered incense." - (Num 16:32-35 KJV)
What was actually happening was man's opposition against God's plan for a mediator. Comparisions were being made and justification (for them to be in the place of Moses) were made, "Doesn't God also speak by [through] us?" -and- "All the congregation is holy" (not just YOU)" -- this offense was against the Plan of God and against the One Mediator, as 1Tim 2:5 states, "For there is one God, and one mediator between God and men, the man Christ Jesus." Aaron did sin, but he immediately saw what God had done and aligned himself in Christ by intercession. Clearly then, God is no respector of persons, but He does look upon the heart.