The way I see it, if there's no sign, it's okay until told otherwise by an employee. I won't seek out an employee to ask, though.
Washington law says private businesses may bar CC, but they have to tell you, not the other way around. A sign is the simplest way. You have no duty to ask.
A private business is *NOT* "public". The law differentiates completely between "public" places and "private" places. A business may be "open to the public" but it is not "a public place". A private business may bar anyone from entering for nearly any reason (certain civil rights laws obviously limit certain discrimination methods.) That business doesn't like your blue baseball cap? You're out. If they put a sign stating such on their door, and you walk in, you are agreeing to the terms posted. By entering with a blue hat, you are purposefully violating their conditions for entering their business.
I assume you would want visitors to your home to obey your requirements for entry, regardless of what they might be. For example, maybe you have kids and a fairly "conventional" world view, and a male friend comes in wearing nothing but a G-string. You're fully within your rights to get pissed off at him and refuse him entry. Other people have the same feelings about guns. My sister is one of them. When my grandmother gave me my grandfather's 1940s-era shotgun for Christmas a few years ago, my sister left the room as soon as she figured out what was in the case, until I put it in my car. Which is exceptionally stupid because at the time, she dealt with police officers all day.
Now, I avoid Wal-Mart for other reasons, but I also make a point of avoiding businesses that have signs up barring potential customers because of arbitrary, non-safety-related reasons. I can understand "no masks or non-prescription sunglasses" at a bank. "No firearms" at a Wal-Mart? Goofy.
As someone else has written on a similar thread before "Why give our hard earned money to idiots who dont want us in their store?"
Edit: Wow, somehow when I started replying, I didn't notice how old and long this thread was... I think I'll have to go read the whole thread now and hope I don't have something completely different to say.....