I think it's more than that.
When a tzibur has guys going off for their third, fourth etc round of miluim... missing their families, work, kollel... at some point they start to be just a little less accepting of our claim to a right to an exemption just for being registered in a yeshiva.
There's a lack of coherent messaging (and possibly opinion) as to the REASON an exemption is wanted. I think this should be split into two categories:
1. People who are actually learning in Yeshivos (and Kollelim)
2. Rejection of draft due to העברה על הדת, regardless of learning status.
When there is no clear message regarding issue #2, there is increased resentment in the general public regarding issue #1. This is exacerbated by the very weak (to say the least) stance regarding "judicial reform". There are many in the IDF and in the government who are willing and eager to create a system where העברה על הדת would not be a concern. However, as long as the Juristocracy is in control, it can deteriorate very quickly, and promises and best intentions will be undone.
Just claiming a "special class" of people (what exactly is the definition?) called "Charedi" that will get an automatic exemption or special treatment, without explaining #2 above AND ITS INTERCONECTEDNESS WITH "JUDICIAL REFORM" is guaranteed to create resentment.