I customised my biblatex citation to look exactly how I want them to look, except the comma in \citep should have the same color as the link. (It does not matter if the comma is actually inside the hyperlink or if it will just have the same color)
MWE:
\documentclass{book}
\usepackage{xcolor}
\usepackage[
style=authoryear,
natbib=true,
]{biblatex}
\addbibresource{Thesis.bib}
% modify \cite to add parenthesis around the year
\renewbibmacro*{cite}{%
\iffieldundef{shorthand}{%
\ifthenelse{%
\ifnameundef{labelname}\OR\iffieldundef{labelyear}%
}{%
\usebibmacro{cite:label}%
\setunit{\addspace}%
}{%
\printnames{labelname}%
\setunit{\addspace}%
}%
% \ifentrytype{online}{\addspace \textendash\addspace\usebibmacro{title}}{%
\printtext[parens]{\usebibmacro{cite:labeldate+extradate}}%
% }%
}%
{\usebibmacro{cite:shorthand}}%
}
\DeclareCiteCommand{\cite}
{\usebibmacro{prenote}}
{\usebibmacro{citeindex}%
\printtext[bibhyperref]{\usebibmacro{cite}}}
{
% \multicitedelim
\textcitedelim
}
{\usebibmacro{postnote}}
\DeclareCiteCommand{\citep}[\mkbibparens]{%
\usebibmacro{prenote}%
}{%
\usebibmacro{citeindex}%
\iffieldundef{shorthand}{%
\ifthenelse{%
\ifnameundef{labelname}\OR\iffieldundef{labelyear}%
}{%
\usebibmacro{cite:label}%
\setunit{\addspace}%
}{%
\printtext[bibhyperref]{% Apply citation link to bibmacro output
\DeclareFieldAlias{bibhyperref}{default}%
\printnames[labelname_p]{labelname}%
\setunit{\nameyeardelim}%
}
}%
\usebibmacro{cite:labeldate+extradate}%
}{%
\usebibmacro{cite:shorthand}%
}%
}{%
% \multicitedelim%
\ifnumequal{\value{citecount}}{\value{citetotal}}
{\addspace\bibstring{and}\addspace}%
{\multicitedelim}%
}{%
\usebibmacro{postnote}%
}
\usepackage{hyperref}
\hypersetup{
colorlinks=true,
citecolor=red,
}
\begin{filecontents}{Thesis.bib}
@ARTICLE{2019arXiv190606091W,
author = {{Wolf}, C. and {Langer}, C. and {Montes}, F. and {Pereira}, J. and
{Ong}, W. -J. and {Poxon-Pearson}, T. and {Ahn}, S. and {Ayoub}, S. and
{Baumann}, T. and {Bazin}, D.},
title = "{Constraining the Neutron Star Compactness: Extraction of the $^{23}$Al($p,\gamma$) Reaction Rate for the $rp$-Process}",
journal = {arXiv e-prints},
keywords = {Nuclear Experiment, Astrophysics - Instrumentation and Methods for Astrophysics, Astrophysics - Solar and Stellar Astrophysics, Nuclear Theory},
year = "2019",
month = "Jun",
eid = {arXiv:1906.06091},
pages = {arXiv:1906.06091},
archivePrefix = {arXiv},
eprint = {1906.06091},
primaryClass = {nucl-ex},
adsurl = {https://ui.adsabs.harvard.edu/abs/2019arXiv190606091W},
adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}
\end{filecontents}
\begin{document}
\cite{2019arXiv190606091W}
\citep{2019arXiv190606091W}
\citep[this text][and this text should remain black]{2019arXiv190606091W}
\printbibliography
\end{document}


authorandyearfields. (Aside: I think that the separator comma is unnecessary and shouldn't be there.) Making the parentheses in the parenthetic-style citation call-out part of the hyperlink would also restore visual parity with the text-style citation call-out. – Mico Jun 21 '19 at 13:35