Does Islam allow getting married in the month of Muharram or Safar?

All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.

Marriage is lawful at any day of the year and there is no evidence in the Sharee’ah that supports the opinion in your question. Rather, such an opinion is a form of falsehood.

A Muslim is not allowed to listen to false impressions and doubts that are circulated among the mob.

In this vein, the Prophet said: “There is neither infection nor evil omen.” [Al-Bukhari and Muslim]

The Prophet also said: “An evil omen is a form of Shirk.” [Abu Dawood and Ibn Majah]

This means that choosing a particular day or month does not change the Predestination or Divine Decree, which brings bad or good.

Allah knows best.