Baposter Boxheader Vertical Alignment

The default header boxes have 0pt depth. This is the default for any node (see section 5.1 of the TikZ manual). To align letters on the baseline, you need to add text depth = 0.25ex to the macro that creates the headerbox. It is the same issue as here: How to “fix baselines” in tikz nodes?

documentclass[landscape,a4paper]{baposter}

makeatletter
renewcommand{baposter@box@headerdrawtext@rectangle}[1]{
  path (baposter@box@name nw) + (0em,-0.5baposter@box@@boxheaderheight)
        node[anchor=west,inner sep=0.4em,text depth=0.25ex] {#1};% <-- added text depth
}
makeatother

begin{document}

begin{poster}{
  grid=false,
  columns=2,
  colspacing=4.2mm,
  headerheight=0.10textheight,
  background=none,
  eyecatcher=false,
  %posterbox options
  headerborder=closed,
  borderColor=red,
  headershape=rectangle,
  headershade=plain,
  headerColorOne=blue,
  textborder=rectangle,
  boxshade=plain,
  boxColorOne=white,
  headerFontColor=white,
  headerfont=color{white}largebfseriessffamily,
  textfont=normalsizesffamily,
  linewidth=1pt
}
{}
{Title}
{textsc{Author}}
{}

begin{posterbox}[name=box1,column=0,row=0,span=1]{M}
Hello
end{posterbox}

begin{posterbox}[name=box2,column=1,row=0,span=1]{Mp}
Hello
end{posterbox}

end{poster}

end{document}