Are sensory receptors neurons?
Short answer  

Receptor cells are specialized neurons


Background  

There are, globally, three types of neurons (Eckert's Animal Physiology):


Sensory neurons: these cells transmit information from external stimuli (e.g., sound, light, pressure), or from internal stimuli (e.g., blood oxygen level or head orientation);
Interneurons: these cells connect other neurons within the central nervous system;
Motor neurons: these neurons carry effector signals to effector organs, causing contraction of muscles or secretion by gland cells.


To illustrate these classes of neurons let's consider the visual peripheral system. Fig. 1 shows a schematized representation of the retinal circuitry, connecting the photoreceptors to the ganglion cells of the optic nerve (interneurons):



Source: Instituto Balseiro

The photoreceptor's response is graded. Notably, the bipolar cell, being an interneuron has also a graded response. The bipolar cells convey the signal, in turn, to the ganglion cells that translate the analog, graded signals into a binary, neural spiking code that enters the optic nerve.  

Receptor cells are considered neurons, but they are highly specialized. Although interneurons may come in various shapes and sizes, they are not so specialized as receptor cells. The photoreceptor, for example, has a highly specialized dendritic region containing the photosensitive pigment and membrane stacks that capture light.  

Another receptor is the Pacinian corpuscle, a vibrotactile mechanoreceptor of the skin:


  Source: Pixgood

In this case, the receptor cell is in fact a myelinized and spiking neuron that functionally much resembles an interneuron. Just as the photoreceptor, the dendritic part does not connect to another neuron, but is highly specialized structure designed to sense a physical external stimulus. In case of the Painian corpuscle, it is an onion-like structure consisting of many lamina. These lamellar structures substantially change the receptor's response to mechanical stimuli. Specifically, it allows the corpuscle to respond rapidly to pressure changes and allow it to faithfully transmit vibratory stimuli.


Reference 

 
Eckert, Animal Phsyiology:
 - Chapter 5 - The Physiological basis of Neuronal Function
 - Chapter 7 - Sensing the Environment