How does conjugation affect reactivity?
The effect of conjugation on electrophilicity and nucleophilicity of chemical species varies depending on the type of conjugation. There is no contradiction between the two cases you have presented in your question because in each case, the conjugation at work is different. 

The conjugation which occurs in conjugated polyenes has been well elaborated upon by Philipp (and thus, I shall not elaborate further), in the answer you have linked to. This type of conjugation occurs as a result of interactions between parallel p orbitals in a chain of carbon atoms. 

The other sort of conjugation you mentioned reading in the book by Keeler and Wothers is an interaction involving an interaction between the nonbonding molecular orbital, which holds the lone pair, localised on ${X}$ (e.g. $\ce {NH2,Cl, Br}$) and the antibonding $\pi$ molecular obital of the $\ce {C=O}$ bond, which is more localised on $\ce {C}$. This is a $\ce {HOMO-LUMO}$ interaction between the two orbitals and electron density is donated into the antibonding $\pi$ MO from the nonbonding MO on $X$. This interaction produces yet another set of bonding and antibonding molecular orbitals. Since the bonding MO produced is of a lower energy than the nonbonding MO on $X$, the lone pair is stabilised and its reactivity is decreased. Also, since the antibonding MO produced is of a higher energy than the previous antibonding MO of the $\ce {C=O}$ bond, the LUMO is raised in energy as a result, decreasing reactivity of the carbonyl group towards nucleophiles. One of the consequences of this conjugation is the lower reactivity of amides towards nucleophilic addition (Clayden et al., 2012).

Reference

Clayden, J., Greeves, N., &amp; Warren, S. (2012). Organic Chemistry (2nd ed.). New York : Oxford University Press Inc.