Is it acceptable for a lecturer to refuse to allow their qualifications and work experience to be placed on a university website?
Sure it is acceptable for a Lecturer to refuse to do this, given that it isn't a condition of the Lecturer's being hired that they agree to publicly posting the information, nor is doing so strictly required for the lecturer to do the other parts of the job that are required. 

My own view is that it'd be crazy not to make your information publicly available, since there's no harm in doing so, but much harm in terms of lost opportunities from not doing it. Still, there's no legal or even moral prohibition against making poor career choices.