How to ignore kerning of underbrace in math mode

In this particular case \mathclap is not necessary:

\documentclass{article}
\usepackage{amsmath}

\begin{document}

\begin{equation*}
x{\underbrace{(4-3y)}_{\substack{\text{positive}\\[1pt] \forall y \in [0,1]}}} + 4y - 1
\end{equation*}

\end{document}

Compare with

\documentclass{article}
\usepackage{amsmath,mathtools}

\begin{document}

\begin{equation*}
x{\underbrace{(4-3y)}_{\mathclap{\text{positive $\forall y \in [0,1]$}}}} + 4y - 1
\end{equation*}

\end{document}

Note, anyway, the additional pair of braces around the whole

{\underbrace{...}_{...}}

construction: they're necessary in order to get the right spacing.

The subscript can be set in a zero-width box. The size of the subscript should be set explicitly. This results in the same output as \mathclap from mathtools.

MWE:

\documentclass{article}
\usepackage{amsmath}
\usepackage{mathtools}
\begin{document}
\begin{align}
    &x
   \underbrace{(4-3y)}_
    {\text{Positive $\forall y \in [0,1]$}}
    +4y -1
\end{align}
\begin{align}
    &x
   \underbrace{(4-3y)}_
    {\makebox[0pt]{\scriptsize\text{Positive $\forall y \in [0,1]$}}}
    +4y -1
\end{align}
\begin{align}
    &x
   \underbrace{(4-3y)}_
    {\mathclap{\text{Positive $\forall y \in [0,1]$}}}
    +4y -1
\end{align}
\end{document}

Result: