With unicode-maths
, use the [range=it->up]
option. Compile with xelatex/lualatex.
Presumably you aren't using 𝕽 anywhere.

MWE
\documentclass{article}
\usepackage{amsmath}
\usepackage{xcolor}
\usepackage{unicode-math}
\newcommand\mfname{Asana Math}
\setmainfont[Colour=blue]{\mfname}
\setmathfont{\mfname}
\setmathfont{XITS Math}[Colour=red,range={it->up}]
\usepackage{simpsons}
\begin{document}
Unicode (math mode):
$𝒢^{2} ∈ 𝕽_{θ_{i}}$
Unicode (text mode):
{\huge
𝒢\hspace{2pt}\textsuperscript{\normalsize 2} ∈ 𝕽\textsubscript{\Large{θ}\textsubscript{\textit{i}}}
}
\hfill\Left\Burns
x + \mscrL + \BbbN + \mfrakH + \mbffrakR \ $\mapsto$ \ $x + \mscrL + \BbbN + \mfrakH + \mbffrakR $
\bigskip
egreg: This document has upright math $a+b=c$ everywhere. It's so bad
that my eyes bleed.
\begin{equation}\label{xx}
\begin{split}
a& =b+c-d\\
& \quad +e-f\\
& =g+h\\
& =i
\end{split}
\end{equation}
A more complicated display
\begin{equation}\label{e:barwq}\begin{split}
H_c&=\frac{1}{2n} \sum^n_{l=0}(-1)^{l}(n-{l})^{p-2}
\sum_{l _1+\dots+ l _p=l}\prod^p_{i=1} \binom{n_i}{l _i}\\
&\quad\cdot[(n-l )-(n_i-l _i)]^{n_i-l _i}\cdot
\Bigl[(n-l )^2-\sum^p_{j=1}(n_i-l _i)^2\Bigr].
\end{split}\end{equation}
\end{document}
Plenty of math alphabets in Unicode, all in the one font file. Here are some:

mathastext
package? Please also provide information about the TeX engine (pdfLaTeX? XeLaTeX? LuaLaTeX? something else?), the document class, and any font packages you employ.