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, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.
You do not have to wash the new Ihraam clothes, because the basic principle is that they are ritually pure until proven otherwise (with certainty). In principle, a new garment is ritually pure; it is lawful to assume Ihraam or perform the prayer while wearing it even if it has not been washed, and even if it was made by a non-Muslim.
Khaleel's book Al-Mukhtasar reads, "It is impermissible to perform the prayer wearing the clothes of a non-Muslim, contrary to what is the case regarding clothes which were made by a non-Muslim..." Muslim scholars underlined that the clothes made by a non-Muslim for himself or others are ruled to be pure. Al-Hattaab said, "It is permissible to pray while wearing them, according to the consensus of scholars." [Mawaahib Al-Jaleel] Al-Mawwaaq said, "This was the practice of the righteous people."
As for washing them as a gesture of respect for Makkah and Madeenah, this is not advisable in order to avoid immoderation and excessiveness, which are dispraised in the Shariah, and because this was not the practice of the righteous predecessors as far as we know.
We ask Allah to guide you, help you, and accept your worship.
Allah knows best.