Generally, legally, no, not just for ignoring a “no soliciting” sign.

But they’re presumably trespassing.

And, despite what ideas you may get from the media, mere trespass without imminent threat to life is not a justification for deadly force.

There are some states where the considerations for self defense do not include a duty to retreat if possible, either in general (“stand your ground" law) or specifically in the home (“castle doctrine"), but all the other requirements (imminent threat of certain kinds of serious harm, proportional force) for self-defense remain part of the law in those states, and trespassing by/while disregarding a ”no soliciting” would not, by itself, satisfy those requirements.