I said nothing of Ayn Rand
Not directly, no, but you were espousing the same philosophies she championed.
The Atheists asked if they could wear their T-Shirts, the Christians said no. The Atheists said that was fine, and still wanted to help and were still rejected by the Christians.
Indeed. In fact, it would have been overall better for the ministry's own evangelism goals to accept them.
If they had said "okay, you can help, but you can't wear your t-shirts, you can't try to convert people to atheism, and you can't try to undermine our attempts to evangelize", and they said okay, then they would have more people serving the food, and thus more people coming in for it, and more people to evangelize to. If the atheists went back on their agreement and tried to break any of the conditions, it would make them look bad.
Instead, by rejecting their offer, the atheist group instead set up their own operation to feed the poor, where I presume they wore their tshirts and told people about their cause, not only being a rival to the Christian soup kitchen but spreading their beliefs, which they wouldn't have been doing if they were allowed to help. And on top of that, the Christian rejecting them made them look bad.
Overall the decision to reject them was a bad idea and ended up worse for them.