Yes, but with some limits. It is possible to wash bagless vacuum filters in water or with soap.
However it has some limits. First of all the fabric must be safe for washing in water. Most bagless vacuum filters are made from paper fibers, so they can only be washed in mild detergents without bleach and have to be dried out afterward. Fabric made from synthetic material can’t be washed again because it will damage the filter cloths which are usually glued together with a special glue that becomes soft when wetted (this is also true for wool).
Note: It is recommended to read the manual instructions or contact the manufacturer for further details regarding washing of bagless vacuum filter.