Our parish posted the availability of "gluten free hosts." Is this not another diminishment of the true presence? How could the Body of Christ make anyone sick?

So called “gluten free hosts” are not utterly free of all gluten. There are still some trace amounts. The US Bishops Conference allows the use of very low gluten hosts and urges additional caution by listing three reputable suppliers of them on the USCCB website. 
 
As for the Blessed Sacrament making someone sick, it is not the Sacrament that does so, but the “accidents.” While your acknowledgement of the True Presence is laudable, it is important to remember that Catholic teaching states that though the bread is transubstantiated, the “accidents” remain. 
 
The "accidents" are the physical attributes of the bread and wine ‐ that is, what can be seen, touched, tasted, or measured. These remain, though the substance of bread and wine change to become the Body, Blood, Soul and Divinity of Jesus. Hence it does not follow that one could not be affected by gluten in a consecrated Host, or by alcohol in the consecrated Blood, for these attributes remain to our senses.