Do my clothes become unpure if a non-Muslim's sweaty clothes come in contact with mine?

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, sallallahu ‘alayhi wa sallam, is His slave and Messenger.

Clothes are not defiled by coming in contact with any person's sweat, even if this person is a non-Muslim, because the perspiration of the human being is ritually pure.

The Kuwaiti Encyclopedia of Fiqh reads, "The scholars held that the perspiration of human beings is absolutely pure, and there is no difference in this regard between the Muslim and the non-Muslim, the intoxicated (drunk) and the sober person, or the menstruating woman and the one in a state of Janaabah (major ritual impurity)..."

It was authentically narrated in Saheeh Al-Bukhaari and Saheeh Muslim that the Prophet, sallallahu ‘alayhi wa sallam, performed ablution from a water container belonging to a polytheist woman. He tied up Thumaamah ibn Uthaal when he was a disbeliever to a pillar in the mosque. He ate from the goat gifted to him by a Jewish woman from Khaybar. He ate the cheese brought from the lands of the Christians, as narrated by Ahmad and Abu Daawood on the authority of Ibn ‘Umar, may Allah be pleased with him. He, sallallahu ‘alayhi wa sallam, also ate barley bread and rancid fat offered to him by a Jewish man. The verse in Soorah Al-Maa'idah, which was the last verse to be revealed in this regard, underlined that it is lawful for the Muslims to eat the food of the People of the Book and marry their (chaste) women. Moreover, the Prophet, sallallahu ‘alayhi wa sallam, served food to the delegation of the disbelievers without washing the vessels, nor did he give his orders to have them washed. It was not reported that our righteous predecessors used to avoid the moisture of the non-Muslims. Had they avoided it, it would have been widely reported.

Allah knows best.