I think it carries some rhetorical weight. ICE is a political paramilitary organisation and as it serves no legitimate civic or legal function outside of that purpose it's entirely wrapped up IN the politics behind it and attempts to invoke some legitimacy through that. It is because of that political support from some of the populace that such a force can exist and do what it does without uniform discontent and disapproval from the population suffering under their activities.Those particular segments subscribing to those particular politics have, as part of the wider constellation of beliefs, admiration for and an idealistic appreciation of the traditional military and those who are or have been a part of it (as long as they're quiet and don't say anything inconvenient).

When even former or serving military veterans get victimised it does make it look at least a little bit worse to a wider range of people than it otherwise might. ICE supporters will certainly have ideological defences and rationalisations for this, they'll surely rapidly disown military personnel who don't toe the line and attempt to discredit them, but is at least a little bit inconvenient having to do this compared to just cheering on the oppression as part of a righteous attack on undesirable elements as any other victims will be considered.