Can axons act as receptors?
Short answer
The textbooks are right; the receptor part of sensory neurons is always considered to be the dendrite. Axons are nonetheless an integral part of some receptor types to send the signal to the brain. Other, more specialized sensory cells do not have an axon and therefore rely on secondary neurons to send the signal to the brain. 

Background
There are three types of sensory cells, namely those with free nerve endings, those with specialized dendritic structures, and specialized receptor cells that synapse directly onto a secondary neuron (Fig. 1).


Fig. 1. Types of sensory neurons. Source: Premed HQ. 


Sensory neurons with free nerve endings have an exposed dendrite that functions as receptor. Examples are nociceptors (pain receptors) and hair follicle receptors.
Other sensory neurons are complex cells that feature a dendritic region specialized for a particular receptor function. Examples are the Pacinian corpuscle and olfactory neurons.
The most common receptor type are specialized receptor neurons that have no axon and need a secondary sensory neuron to send the signal to the brain. Examples are the photoreceptor cells in the retina, the hair cells in the cochlea and Merkel cells.