baskervald (Baskerville) font out of alignment

You can change the protrusion at the margin with microtype:

\documentclass{article}
\usepackage[T1]{fontenc}
\usepackage{baskervald}
\usepackage{lipsum,microtype}
\parindent 0pt
\SetProtrusion
 [load= default,context = testJ]
 { encoding = T1,
  family = ybv }
 { J = {-500,},
 }

\begin{document}
J shows protrusion; \\ABC

\begin{microtypecontext}{protrusion=testJ}
J shows protrusion; \\ABC
\end{microtypecontext}

\end{document}

As I commented, I think the font designer intended this for the letter "J". In the MWE, I show the protrusion of a leading "J", I show its bounding box, which makes it easier to understand why it protrudes, and I show it in combination with other letters, which might explain why the font designer wanted it this way (the AJ combo does look cool).

I show on the next two lines how one can manually compensate, by leading with a \,J (while in horizontal mode).

\documentclass{article}
\usepackage{baskervald,lipsum}
\parindent 0pt
\begin{document}
J shows protrusion; \fboxsep=-\fboxrule\fbox{J} shows bounding box; AJ shows kerning

A shows non-protruding letter

\leavevmode\,J artificially compensates for protrusion

\lipsum[1]

\end{document}

Thus, in conclusion, one's options are limited. I think one has to learn to embrace the choice of the font designer and just go with it.

Maybe a very old post, but... Like most the fonts I gave to the free publication and free design community, the aim was to offer alternative fonts not to copy them. So, Baskervald is not Baskerville, Gillius is not Gill Sans etc., they have there own identity. That explains why the J glyph is a design choice, a style effect. That said, it's always possible to add an alternative J glyph in a future Baskervald font revision. Regards