Distorted circles in axis environment with TikZ

pgfplots uses undocumented internal TikZ commands, which have recently changed. I was promised a fix by the maintainer but so far nothing is forthcoming.

https://sourceforge.net/p/pgfplots/bugs/232/

\documentclass{article}
\usepackage{pgfplots}
\pgfplotsset{compat=1.16}

\makeatletter
\def\pgfplots@install@path@replacements{%
    \ifpgfplots@path@replace@ellipse
        \let\tikz@do@circle=\pgfplots@path@@tikz@do@circle
        \let\tikz@do@ellipse=\pgfplots@path@@tikz@do@circle
        \expandafter\def\expandafter\pgfinterruptpicture\expandafter{\pgfinterruptpicture
            \let\tikz@do@circle=\pgfplots@path@@tikz@do@circle@orig
            \let\tikz@do@ellipse=\pgfplots@path@@tikz@do@ellipse@orig
        }%
    \fi
}%
\let\pgfplots@path@@tikz@do@circle@orig=\tikz@do@circle
\let\pgfplots@path@@tikz@do@ellipse@orig=\tikz@do@ellipse

\let\pgfplots@path@@tikz@do@circle@oldandbroken=\pgfplots@path@@tikz@do@circle
\def\pgfplots@path@@tikz@do@circle#1{\pgfplots@path@@tikz@do@circle@oldandbroken{#1}{#1}}
\def\pgfplots@path@@tikz@do@ellipse#1#2{\pgfplots@path@@tikz@do@circle@oldandbroken{#1}{#2}}
\makeatother

\begin{document}

\begin{tikzpicture}
\begin{axis}[
  ymin=-3, ymax=3,
  xmin=-3, xmax=3
]

\draw (1,0) circle [radius=1.5];
\fill (1,0) circle [radius=1];

\end{axis}
\end{tikzpicture}

\end{document}

You need to use axis equal. If the values of 1 unit on both of the axis are not equal the resulting image won't be a circle.

The first image below is the original, the second one has axis equal applied:

Code:

\documentclass{article}
\usepackage{pgfplots}
\pgfplotsset{compat=1.16}

\begin{document}

\begin{tikzpicture}
\begin{axis}[
  ymin=-3, ymax=3,
  xmin=-3, xmax=3,
]

\draw (1,0) circle [radius=1.5];
\fill (1,0) circle [radius=1];

\end{axis}
\end{tikzpicture}
\begin{tikzpicture}
\begin{axis}[
  ymin=-3, ymax=3,
  xmin=-3, xmax=3,
  axis equal,
]

\draw (1,0) circle [radius=1.5];
\fill (1,0) circle [radius=1];

\end{axis}
\end{tikzpicture}

Listfiles

 article.cls    2019/10/25 v1.4k Standard LaTeX document class
  size10.clo    2019/10/25 v1.4k Standard LaTeX file (size option)
pgfplots.sty    2018/03/28 v1.16 Data Visualization (1.16)
graphicx.sty    2017/06/01 v1.1a Enhanced LaTeX Graphics (DPC,SPQR)
  keyval.sty    2014/10/28 v1.15 key=value parser (DPC)
graphics.sty    2019/11/01 v1.3d Standard LaTeX Graphics (DPC,SPQR)
    trig.sty    2016/01/03 v1.10 sin cos tan (DPC)
graphics.cfg    2016/06/04 v1.11 sample graphics configuration
  pdftex.def    2018/01/08 v1.0l Graphics/color driver for pdftex
    tikz.sty    2019/08/03 v3.1.4b (3.1.4b)
     pgf.sty    2019/08/03 v3.1.4b (3.1.4b)
  pgfrcs.sty    2019/08/03 v3.1.4b (3.1.4b)
everyshi.sty    2001/05/15 v3.00 EveryShipout Package (MS)
pgfrcs.code.tex
 pgfcore.sty    2019/08/03 v3.1.4b (3.1.4b)
  pgfsys.sty    2019/08/03 v3.1.4b (3.1.4b)
pgfsys.code.tex
pgfsyssoftpath.code.tex    2019/08/03 v3.1.4b (3.1.4b)
pgfsysprotocol.code.tex    2019/08/03 v3.1.4b (3.1.4b)
  xcolor.sty    2016/05/11 v2.12 LaTeX color extensions (UK)
   color.cfg    2016/01/02 v1.6 sample color configuration
pgfcore.code.tex
pgfcomp-version-0-65.sty    2019/08/03 v3.1.4b (3.1.4b)
pgfcomp-version-1-18.sty    2019/08/03 v3.1.4b (3.1.4b)
  pgffor.sty    2019/08/03 v3.1.4b (3.1.4b)
 pgfkeys.sty    
pgfkeys.code.tex
 pgfmath.sty    
pgfmath.code.tex
pgffor.code.tex
tikz.code.tex
supp-pdf.mkii
epstopdf-base.sty    2016/05/15 v2.6 Base part for package epstopdf
infwarerr.sty    2016/05/16 v1.4 Providing info/warning/error messages (HO)
  grfext.sty    2016/05/16 v1.2 Manage graphics extensions (HO)
kvdefinekeys.sty    2016/05/16 v1.4 Define keys (HO)
 ltxcmds.sty    2016/05/16 v1.23 LaTeX kernel commands for general use (HO)
kvoptions.sty    2016/05/16 v3.12 Key value format for package options (HO)
kvsetkeys.sty    2016/05/16 v1.17 Key value parser (HO)
etexcmds.sty    2016/05/16 v1.6 Avoid name clashes with e-TeX commands (HO)
ifluatex.sty    2019/10/25 v1.5 ifluatex legacy package. Use iftex instead.
   iftex.sty    2019/11/07 v1.0c TeX engine tests
pdftexcmds.sty    2019/07/25 v0.30 Utility functions of pdfTeX for LuaTeX (HO)
   ifpdf.sty    2019/10/25 v3.4 ifpdf legacy package. Use iftex instead.
epstopdf-sys.cfg    2010/07/13 v1.3 Configuration of (r)epstopdf for TeX Live