This not a question, just something that might be helpful to others. With Plots 1.12 and GR0.57.4 (at least), and using these options below, one can get a plot with homogeneous fonts (“Computer Modern”) in every element.
using Plots
using LaTeXStrings
plot_font = "Computer Modern"
default(fontfamily=plot_font,
linewidth=2, framestyle=:box, label=nothing, grid=false)
scalefontsizes(1.3)
plot(sort(rand(10)),sort(rand(10)),label="Legend")
plot!(xlabel=L"\textrm{Standard text}(r) / \mathrm{cm^3}")
plot!(ylabel="Same font as everything")
annotate!(0.2,0.8,text("My note",plot_font,12))
savefig("./plot.pdf")
Previously
const plot_font = "Computer Modern"
const PLOTS_DEFAULTS = Dict(:theme=>:default,
:fontfamily => plot_font,
:linewidth => 2,
:framestyle => :box,
:label => "",
:grid => false)
using Plots
using LaTeXStrings
plot(sort(rand(10)),sort(rand(10)),label="Legend")
plot!(xlabel=L"\textrm{Standard text}(r) / \mathrm{cm^3}")
plot!(ylabel="Same font as everything")
annotate!(0.2,0.8,text("My note",plot_font,12))
savefig("./plot.pdf")
Additionally, some basic latex is good to know:

\textm
removes the math mode from a latex string. 
\mathrm
removes the italics (not math mode) from the latex string, such that, for example, the exponent looks nicely placed in a nonitalic string.
What I would like sometimes is to change everything to sffamily
fonts. But that I was unable to do consistently yet.