The reason for the differing space here is a combination of factors. First, because the first plot is wider than the two last, the distance from the right side of the axis to the edge of the subfigure is smaller for the first than for the last two.
Further, the two last plots are narrower than the subfigure environments, and by default text inside these are aligned to the left. To fix that part, add \centering at the start of each subfigure environment, but that isn't enough to get equal distance between axis 1&2 and 2&3, due to what is described in the first paragraph above.
Now, there might well be other ways, I'm definitely not good at finding elegant solutions, but the workaround I thought of is to use \begin{tikzpicture}[trim axis left] for all three plots. trim axis left is a style that changes the bounding box of the tikzpicture so that anything to the left of the axis (ticklabels, ylabel) are not considered when determining the bounding box. This does have the unwanted side effect that the ticklabels of the first axis may go into the left margin, but you can counter that by adding some horizontal space before the first subfigure. (See code example below.)
I also made the subfigures a bit narrower and used \hfill between them to add space that fills out the line.
That said, if you are not going to add individual captions, then I would say you using the wrong tool for the job, and making the code longer than necessary. I would suggest adding the groupplots library of pgfplots, and adding all three images in the same groupplot environment. (I didn't think of this for your previous question.) groupplots makes this sort of thing very easy to do.
With the help of \captionof from the caption package you can also add subcaptions, by placing \nodes with a specified text width relative to the axes, example below. Some juggling with the figure counter seems to be needed to get correct cross references though.
\RequirePackage{luatex85}
\documentclass{article}
\usepackage{pgfplots,caption,subcaption,showframe}
\captionsetup[subfigure]{labelformat=parens}
\usepgfplotslibrary{groupplots}
\pgfplotsset{compat=newest}
\usepackage{cleveref}
\begin{document}
\begin{figure}
\centering
\begin{tikzpicture}
\begin{groupplot}[
group style={
group name=G,
group size=3 by 1,
y descriptions at=edge left,
horizontal sep=10pt % adjust as needed
},
enlargelimits=false,
width=0.33\textwidth-width("300"),
height=0.3\textheight,
scale only axis]
\nextgroupplot
\addplot graphics [xmin=0, xmax=50, ymin=0, ymax=150] {example-image-a};
\nextgroupplot
\addplot graphics [xmin=0, xmax=50, ymin=0, ymax=150] {example-image-b};
\nextgroupplot
\addplot graphics [xmin=0, xmax=50, ymin=0, ymax=150] {example-image-c};
\end{groupplot}
\refstepcounter{figure} % to get correct
\node [text width=0.33\textwidth-width("300"),below right,align=center] at (G c1r1.south west) {\captionof{subfigure}{Subcaption for the first plot\label{a}}};
\node [text width=0.33\textwidth-width("300"),below right,align=center] at (G c2r1.south west) {\captionof{subfigure}{Subcaption for the second plot}};
\node [text width=0.33\textwidth-width("300"),below right,align=center] at (G c3r1.south west) {\captionof{subfigure}{Subcaption for the third plot}};
\addtocounter{figure}{-1}
\end{tikzpicture}
\caption{..}
\end{figure}
\begin{figure}
\centering
\pgfmathsetlengthmacro{\myaxiswidth}{0.33\textwidth-width("300 ")}
\hspace*{\dimexpr0.33\textwidth-\myaxiswidth}%
\begin{subfigure}[t]{0.3\textwidth}
\centering % added
\begin{tikzpicture}[trim axis left]
\begin{axis}[enlargelimits=false,width=\myaxiswidth, height=0.3\textheight, scale only axis]
\addplot graphics [xmin=0, xmax=50, ymin=0, ymax=150] {example-image-a};
\end{axis}
\end{tikzpicture}
\caption{Subcaption for the first plot}
\label{b}
\end{subfigure}%
\hfill
\begin{subfigure}[t]{0.3\textwidth}
\centering % added
\begin{tikzpicture}[trim axis left]
\begin{axis}[enlargelimits=false,width=\myaxiswidth, height=0.3\textheight, scale only axis, ytick=\empty]
\addplot graphics [xmin=0, xmax=50, ymin=0, ymax=150] {example-image-b};
\end{axis}
\end{tikzpicture}
\caption{Subcaption for the second plot}
\end{subfigure}%
\hfill
\begin{subfigure}[t]{0.3\textwidth}
\centering % added
\begin{tikzpicture}[trim axis left]
\begin{axis}[enlargelimits=false,width=\myaxiswidth, height=0.3\textheight, scale only axis, ytick=\empty]
\addplot graphics [xmin=0, xmax=50, ymin=0, ymax=150] {example-image-c};
\end{axis}
\end{tikzpicture}
\caption{Subcaption for the third plot}
\end{subfigure}
\caption{...}
\end{figure}
\end{document}
Top is for groupplots code, bottom for subfigure code.
