The prohibition of Kibus applies to clothes and pieces of cloth that absorb dirt. However, wooden furniture and plastic items, which do not absorb dirt, may be cleaned with water to remove dirt that is stuck to them. Based on this, it would seem at first glance that one may clean plastic or nylon tablecloths. Since they are made from one piece of nonabsorbent material, they do not absorb dirt; thus Kibus would not be relevant to them. Indeed, R. Ben-Zion Abba Shaul rules this way in practice (Or Le-Tziyon 2:24:6). However, most poskim maintain that since these tablecloths function the same way as when they are made of cloth, one should be stringent and avoid vigorously scrubbing them as one does when washing clothing. However, since they do not absorb water, one may rinse them and even gently rub them (Igrot Moshe, YD 2:76; Tzitz Eliezer 5:10; Yalkut Yosef 302:22).
Another question arises regarding clothing, a tablecloth, or pantyhose made from synthetic material such as polyester. Everyone agrees that they may not be scrubbed or wrung out, because this would involve cleaning them in the way one normally washes clothing. The question is whether one may rinse them off or soak them in water. Some maintain that since the synthetic material itself does not absorb dirt or water, one may rinse clothing made of such material and even soak it. Soaking would only be forbidden if the clothing was made of natural fibers as well (SSK 15:7-8). Others maintain that even clothing that is fully synthetic may not be soaked; since dirt is absorbed between the threads, when the clothing is soaked or rinsed part of the dirt dissolves and disappears (Or Le-Tziyon 2:24:6). It would seem in practice that one may not soak clothing made from synthetics.
One may clean contact lenses, both hard and soft. The law is more lenient in the case of contact lenses, compared to nylon tablecloths, which may only be lightly scrubbed, because not only are they non-absorbent, they are also not considered clothing, and therefore scrubbing them does not resemble Kibus (see Harĥavot). Similarly, one may clean a pacifier or the nipple of a baby bottle, or scrub it to remove stuck-on dirt. Since they are made out of rubber, Kibus does not apply; and since they do not look like clothing, scrubbing them does not resemble Kibus.