Aligning several \begin{bmatrix*} to have same "column width"

You need different column widths for each column. With an up-to-date TeX distribution you can use the w column type provided by array. But I'm afraid you have to decide the widest entry of each column.

I provide both the right and the center aligned versions; I much prefer the latter.

Avoid trailing \\ as a general rule (unless your alignment has a bottom rule). They do no harm inside array or matrix, they do in align.

\documentclass[10pt,a4paper]{article}
\usepackage[utf8]{inputenc}
\usepackage{amsmath}
\usepackage{mathtools}
\usepackage{array,calc}

\begin{document}

\begin{align*}
\Phi_{1} &=
\begin{bmatrix}
\begin{array}{
  w{r}{\widthof{$\pi$}}
  w{r}{\widthof{$-\pi$}}
  w{r}{\widthof{$-\pi$}}
  w{r}{\widthof{$-\pi$}}
}
0 & -\pi & -\pi & 0 \\
\pi & 0 & 0 & \pi \\
\pi & 0 & 0 & \pi \\
0 & -\pi & -\pi & 0
\end{array}
\end{bmatrix}
&
\Phi_{2} &= 
\begin{bmatrix}
\begin{array}{
  w{r}{\widthof{$\frac{3\pi}{2}$}}
  w{r}{\widthof{$-\pi$}}
  w{r}{\widthof{$-\pi$}}
  w{r}{\widthof{$-\frac{3\pi}{2}$}}
}
0 & 0 & -\pi & -\pi \\
0 & 0 & -\pi & -\pi \\
\pi & \pi & 0 & 0 \\
\pi & \pi & 0 & 0
\end{array}
\end{bmatrix}
\\
\Phi_{3} &= 
\begin{bmatrix}
\begin{array}{
  w{r}{\widthof{$\pi$}}
  w{r}{\widthof{$-\pi$}}
  w{r}{\widthof{$-\pi$}}
  w{r}{\widthof{$-\pi$}}
}
0 & -\pi & 0 & -\pi \\
\pi & 0 & \pi & \pi \\
0 & -\pi & 0 & -\pi \\
\pi & -\pi & \pi & 0
\end{array}
\end{bmatrix}
&
\Phi_{4} &= 
\begin{bmatrix}
\begin{array}{
  w{r}{\widthof{$\frac{3\pi}{2}$}}
  w{r}{\widthof{$-\pi$}}
  w{r}{\widthof{$-\pi$}}
  w{r}{\widthof{$-\frac{3\pi}{2}$}}
}
0 & -\frac{\pi}{2} & -\pi & -\frac{3\pi}{2} \\
\frac{\pi}{2} & 0 & -\frac{\pi}{2} & -\pi \\
\pi & \frac{\pi}{2} & 0 & -\frac{\pi}{2} \\
\frac{3\pi}{2} & \pi & \frac{\pi}{2} & 0
\end{array}
\end{bmatrix}
\end{align*}

\begin{align*}
\Phi_{1} &=
\begin{bmatrix}
\begin{array}{
  w{c}{\widthof{$\pi$}}
  w{c}{\widthof{$-\pi$}}
  w{c}{\widthof{$-\pi$}}
  w{c}{\widthof{$-\pi$}}
}
0 & -\pi & -\pi & 0 \\
\pi & 0 & 0 & \pi \\
\pi & 0 & 0 & \pi \\
0 & -\pi & -\pi & 0
\end{array}
\end{bmatrix}
&
\Phi_{2} &= 
\begin{bmatrix}
\begin{array}{
  w{c}{\widthof{$\frac{3\pi}{2}$}}
  w{c}{\widthof{$-\pi$}}
  w{c}{\widthof{$-\pi$}}
  w{c}{\widthof{$-\frac{3\pi}{2}$}}
}
0 & 0 & -\pi & -\pi \\
0 & 0 & -\pi & -\pi \\
\pi & \pi & 0 & 0 \\
\pi & \pi & 0 & 0
\end{array}
\end{bmatrix}
\\
\Phi_{3} &= 
\begin{bmatrix}
\begin{array}{
  w{c}{\widthof{$\pi$}}
  w{c}{\widthof{$-\pi$}}
  w{c}{\widthof{$-\pi$}}
  w{c}{\widthof{$-\pi$}}
}
0 & -\pi & 0 & -\pi \\
\pi & 0 & \pi & \pi \\
0 & -\pi & 0 & -\pi \\
\pi & -\pi & \pi & 0
\end{array}
\end{bmatrix}
&
\Phi_{4} &= 
\begin{bmatrix}
\begin{array}{
  w{c}{\widthof{$\frac{3\pi}{2}$}}
  w{c}{\widthof{$-\pi$}}
  w{c}{\widthof{$-\pi$}}
  w{c}{\widthof{$-\frac{3\pi}{2}$}}
}
0 & -\frac{\pi}{2} & -\pi & -\frac{3\pi}{2} \\
\frac{\pi}{2} & 0 & -\frac{\pi}{2} & -\pi \\
\pi & \frac{\pi}{2} & 0 & -\frac{\pi}{2} \\
\frac{3\pi}{2} & \pi & \frac{\pi}{2} & 0
\end{array}
\end{bmatrix}
\end{align*}

\end{document}