You can redefine the association of the Greek letters with fonts.
\documentclass{article}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage[greek, english]{babel}
% fix a bad bug in XCharter
\let\LGRtextnu\textnu
\usepackage{XCharter}
% fix a bad bug in XCharter
\let\textnu\LGRtextnu
\usepackage[charter,scaled=1.07]{newtxmath}
\usepackage{substitutefont}
\substitutefont{LGR}{\rmdefault}{artemisia}
\DeclareSymbolFont{greekletters}{LGR}{artemisia}{m}{it}
\SetSymbolFont{greekletters}{bold}{LGR}{artemisia}{b}{it}
\DeclareSymbolFont{ucgreekletters}{LGR}{artemisia}{m}{n}
\SetSymbolFont{ucgreekletters}{bold}{LGR}{artemisia}{b}{n}
\DeclareMathSymbol{\alpha}{\mathord}{greekletters}{`a}
\DeclareMathSymbol{\beta}{\mathord}{greekletters}{`b}
\DeclareMathSymbol{\gamma}{\mathord}{greekletters}{`g}
\DeclareMathSymbol{\delta}{\mathord}{greekletters}{`d}
\DeclareMathSymbol{\epsilon}{\mathord}{greekletters}{`e}
\DeclareMathSymbol{\zeta}{\mathord}{greekletters}{`z}
\DeclareMathSymbol{\eta}{\mathord}{greekletters}{`h}
\DeclareMathSymbol{\theta}{\mathord}{greekletters}{`j}
\DeclareMathSymbol{\iota}{\mathord}{greekletters}{`i}
\DeclareMathSymbol{\kappa}{\mathord}{greekletters}{`k}
\DeclareMathSymbol{\lambda}{\mathord}{greekletters}{`l}
\DeclareMathSymbol{\mu}{\mathord}{greekletters}{`m}
\DeclareMathSymbol{\nu}{\mathord}{greekletters}{`n}
\DeclareMathSymbol{\omicron}{\mathord}{greekletters}{`o}
\DeclareMathSymbol{\xi}{\mathord}{greekletters}{`x}
\DeclareMathSymbol{\pi}{\mathord}{greekletters}{`p}
\DeclareMathSymbol{\rho}{\mathord}{greekletters}{`r}
\DeclareMathSymbol{\sigma}{\mathord}{greekletters}{`s}
\DeclareMathSymbol{\tau}{\mathord}{greekletters}{`t}
\DeclareMathSymbol{\upsilon}{\mathord}{greekletters}{`u}
\DeclareMathSymbol{\phi}{\mathord}{greekletters}{`f}
\DeclareMathSymbol{\chi}{\mathord}{greekletters}{`q}
\DeclareMathSymbol{\psi}{\mathord}{greekletters}{`y}
\DeclareMathSymbol{\omega}{\mathord}{greekletters}{`w}
\DeclareMathSymbol{\varepsilon}{\mathord}{greekletters}{`e}
\DeclareMathSymbol{\vartheta}{\mathord}{greekletters}{`j}
\DeclareMathSymbol{\varpi}{\mathord}{greekletters}{`p}
\DeclareMathSymbol{\varrho}{\mathord}{greekletters}{`r}
\DeclareMathSymbol{\varsigma}{\mathord}{greekletters}{`v}
\DeclareMathSymbol{\varphi}{\mathord}{greekletters}{`f}
\DeclareMathSymbol{\Alpha}{\mathord}{ucgreekletters}{`A}
\DeclareMathSymbol{\Beta}{\mathord}{ucgreekletters}{`B}
\DeclareMathSymbol{\Gamma}{\mathord}{ucgreekletters}{`G}
\DeclareMathSymbol{\Delta}{\mathord}{ucgreekletters}{`D}
\DeclareMathSymbol{\Epsilon}{\mathord}{ucgreekletters}{`E}
\DeclareMathSymbol{\Zeta}{\mathord}{ucgreekletters}{`Z}
\DeclareMathSymbol{\Eta}{\mathord}{ucgreekletters}{`H}
\DeclareMathSymbol{\Theta}{\mathord}{ucgreekletters}{`J}
\DeclareMathSymbol{\Iota}{\mathord}{ucgreekletters}{`I}
\DeclareMathSymbol{\Kappa}{\mathord}{ucgreekletters}{`K}
\DeclareMathSymbol{\Lambda}{\mathord}{ucgreekletters}{`L}
\DeclareMathSymbol{\Mu}{\mathord}{ucgreekletters}{`M}
\DeclareMathSymbol{\Nu}{\mathord}{ucgreekletters}{`N}
\DeclareMathSymbol{\Xi}{\mathord}{ucgreekletters}{`X}
\DeclareMathSymbol{\Omicron}{\mathord}{ucgreekletters}{`O}
\DeclareMathSymbol{\Pi}{\mathord}{ucgreekletters}{`P}
\DeclareMathSymbol{\Rho}{\mathord}{ucgreekletters}{`R}
\DeclareMathSymbol{\Sigma}{\mathord}{ucgreekletters}{`S}
\DeclareMathSymbol{\Tau}{\mathord}{ucgreekletters}{`T}
\DeclareMathSymbol{\Upsilon}{\mathord}{ucgreekletters}{`U}
\DeclareMathSymbol{\Phi}{\mathord}{ucgreekletters}{`F}
\DeclareMathSymbol{\Chi}{\mathord}{ucgreekletters}{`Q}
\DeclareMathSymbol{\Psi}{\mathord}{ucgreekletters}{`Y}
\DeclareMathSymbol{\Omega}{\mathord}{ucgreekletters}{`W}
\begin{document}
Make this \textit{\textgreek{αβγδ}} the same font
as this $\alpha\beta\gamma\delta$.
\textit{\textgreek{αβγδεζηθικλμνξοπρστυφχψω}}
$\alpha\beta\gamma\delta\epsilon\zeta\eta\theta\iota\kappa\lambda
\mu\nu\xi\omicron\pi\rho\sigma\tau\upsilon\phi\chi\psi\omega$
\textgreek{ΑΒΓΔΕΖΗΘΙΚΛΜΝΞΟΠΡΣΤΥΦΧΨΩ}
$\Alpha\Beta\Gamma\Delta\Epsilon\Zeta\Eta\Theta\Iota\Kappa\Lambda
\Mu\Nu\Xi\Omicron\Pi\Rho\Sigma\Tau\Upsilon\Phi\Chi\Psi\Omega$
\end{document}
The “fix for the bad bug in XCharter” is necessary, because the package redefines \textnu, so breaking Greek support.
