In my opinion, the best way to solve this would be by using an expression in the query for your main dataset that evaluates the selection in the hair product parameter. Something like this:

="select customer_id,hairproduct

from inventory where customer_id = @customerid" & IIF(Parameters!hairProduct.value = "", "", " and hairproduct in (@hairproduct);"

I may have something wrong in that expression because it has been awhile since I've used an expression in a dataset query as I usually use stored procedures for my report datasets, but I think that should give you a basic idea of what needs to be done.

Edit: replaced single quoted in expression with double-quotes.