First of all, Democrats are incapable of using 9/11 as either a focal point for their fundamental positions or as a crass partisan tool, so any attempt by them to lay claim to the high ground on this matter is specious.
There is virtually no aspect of 9/11 that they can contend resonates with their message, inspires their direction, or conforms with their world view.
I feel certain they would if they could (witness Katrina) but there is nothing about 9/11 they can exploit
If one contends that Islamic extremism is an existential threat to the West, and believes that US foreign and national security policy should reflect this fact, then invoking the images of 9/11 is not crass exploitation.
Do the Republicans, sometimes, attempt to "make the most" of these images? Probably yes. I feel fairly certain that there are those among the party's political strategists who are prepared to "milk" the images for partisan gain. Such instances are examples of cynical politics and certainly less than honorable, but it's silly to suggest that only Republicans have such cynical operatives, and it's deluded to suggest that any reference to 9/11 is political exploitation.
9/11 was defining moment for this country and many of its citizens. I am one among many who experienced a profound change of perspective after the tragic event.
I understand why Democrats would like to declare 9/11 off limits in political debate, but their desire is based on political interest, not propriety.