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This is an old posting, but I am new here and it caught my eye. Chinese antique sellers frequently call any stone jade, just like they will call any figurine in a turquoise color...turquoise stone. Sometimes they just leave it at turquoise and let you decide!
I have purchased many items from China over the years and with time learned the ins and outs of terminology of Chinese antiques. I have also bought plenty of things that were not what they were claimed until I started reading up on the subject and getting as many Christie's and Sotheby's cataloges as I could to train myself to recognize items as old or as more modern pieces.
I would say that your piece could be soapstone...it comes in many colors, but is a soft and easily workable stone. Your item could be a harder stone. I think those are probably foo dogs. I thought they might be Quilin, but they usually have some sort of horns.
I think you are right about this being a censor. Just to hazard a quess I think it is 19th or 20 century piece. I included a photo of a piece I bought that is soapstone that has had some color added to bring out details. I think it is 20th century, but I'm not really certain. Even if it is not terribly old Chinese pieces are going for higher prices as the Chinese are buying back their history. Veronica