documentclass{book}
usepackage{amsthm}
usepackage{enumitem}
usepackage{xparse}
usepackage{hyperref}

usepackage{lipsum}

newtheoremstyle{fctaylor}% name
  {topsep}%      Space above
  {topsep}%      Space below
  {normalfont}%         Body font
  {}%         Indent amount (empty = no indent, parindent = para indent)
  {bfseries}% Thm head font
  {}%        Punctuation after thm head
  {newline}%     Space after thm head: " " = normal interword space;
  {makethmhead{#1}{#2}{#3}}

newlengthfctaylortheoremindent
AtBeginDocument{setlengthfctaylortheoremindent{3em}} % <- customize here
newlengthfctaylorlabelsep
AtBeginDocument{setlengthfctaylorlabelsep{1em}} % <- customize here

makeatletter
newcommand{makethmhead}[3]{%
  gdefthisthmhead{%
    makebox[fctaylortheoremindent][l]{bfseries#2}%
    {bfseries#1}%
    @ifnotempty{#3}{ (#3)}%
    hspace{fctaylorlabelsep}%
    phantomsection%%% THIS LINE ADDED
  }%
}
makeatother

newenvironment{fctayloritemize}
 {list{}{%
    leftmargin=fctaylortheoremindent
    labelwidth=dimexprfctaylortheoremindent-labelseprelax
    itemindent=0pt
  }}
 {endlist}

NewDocumentCommand{newfctaylortheorem}{smomo}{%
  IfBooleanTF{#1}
   {newtheorem*{fctaylor@#2}{#4}}
   {IfNoValueTF{#3}
     {IfNoValueTF{#5}
       {newtheorem{fctaylor@#2}{#4}}
       {newtheorem{fctaylor@#2}{#4}[#5]}}
     {newtheorem{fctaylor@#2}[fctaylor@#3]{#4}}}%
  NewDocumentEnvironment{#2}{o}
   {IfNoValueTF{##1}{begin{fctaylor@#2}}{begin{fctaylor@#2}[##1]}%
    begin{fctayloritemize}item[thisthmheadhfill]}
   {end{fctayloritemize}end{fctaylor@#2}}%
}

theoremstyle{fctaylor}
newfctaylortheorem{thm}{Theorem}[section]
newfctaylortheorem*{defn}{Definition}

begin{document}
section{One}

begin{defn}
lipsum*[2]
end{defn}

begin{thm}label{A}
lipsum*[2]
end{thm}

begin{thm}[Somebody]label{B}
Something that should show how the text is split across line boundaries
and is correctly indented. And some equivalent conditions:
begin{enumerate}[label=upshape(alph*),ref=(alph*)]
item a condition
item another
item and another
end{enumerate}
which show the point made.

textbf{This line, which begins a new paragraph, should immediately follow the above line but be indented.}
end{thm}

Here are the references: ref{A} and ref{B}.

end{document}

newtheoremstyle{fctaylor}%
  {topsep}%
  {topsep}%
  {normalfont}%
  {}%
  {bfseries}%
  {}%
  {0pt}%     Space after thm head: " " = normal interword space;
  {makethmhead{#1}{#2}{#3}}

newtheoremstyle{fctaylor}%
  {topsep}%
  {topsep}%
  {normalfont}%
  {}%
  {bfseries}%
  {}%
  {newline}%     The one thing I changed which seemed to work in the other answer
  {makethmhead{#1}{#2}{#3}}