Naturalism Habermas rejects is a reductive naturalism. Naturalism is reductive when it ultimately reduces a ‘rational explanation’ to a 'causal explanation'.
This does not necessarily mean that reductive naturalism does not recognize the distinction between ‘causal’ and ‘rational’ explanations. However it believes that, in principle, ‘rational’ can be explained in terms of a ‘causal’ one. Hence a reductive naturalism gives priority to ‘causal’ in the natural order (natural in a broad sense as opposed to supernatural order).
Habermas on the other hand refuses to accept the priority accorded to causal explanation and hence asserts that even in principle ‘rational’ cannot be explained in terms of ‘causal’. He believes in the ultimate irreducibility of the distinction between ‘causal’ and ‘rational’. In this Habermas sides with great idealists, particularly Kant, who reject the claim that ‘reason’ can be explained in terms of ‘causal’.
However Habermas unlike Kant does not posit two worlds or two realms to establish this irreducibility of ‘rational’ to ‘causal’. By refusing to posit world of pure intelligence in order to prove the irreducibility of ‘rational’ Habermas remains within an overall naturalist position, where naturalist is understood in the broad sense.
According to this reading reductionist naturalism is the one which equates ‘natural’ with ‘causal’ and then aspires to explain everything else in terms of ‘causal’. Habermas on the other hand construes ‘natural’ in a broad sense and considers ‘causal’ only one facet of ‘natural’. Accordingly he can claim that ‘rational’ is natural but not ‘causal’. This I believe is the essence of Habermas’ so called ‘weak naturalism’.