Hello, and thank you for your replies.
I do suspect that there may be some sort of "repellent coating" applied to these tactical polo shirts just as most of you have alluded to, even though it says 100% cotton on their labels. I contacted the company yesterday, and their CS person said she would get in touch with the design team and give me a definitive answer.
If I get word back that there is no coating applied and the shirts are pure cotton--and even then I won't be completely certain--perhaps I will try again this weekend, though I will leave the shirts in the eye bath overnight. I'm not sure that Dharma Trading's fiber reactive dyes "work" any better with hot water as opposed to warm, but I will look into it.
Thanks once again.