R, 75 bytes

function(s,x=tabulate(utf8ToInt(tolower(s)),122)[97:122])cat(x[!!x],sep="")

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Prints the result. For invalid input, prints nothing.

Test harness taken from pajonk's answer.

R, 75 72 bytes

function(s,x=tabulate((y=utf8ToInt(s))%%32*(y>64),26))cat(x[!!x],sep="")

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Prints the result. For invalid input, prints nothing.

-3 bytes thanks to Dominic van Essen.

Test harness taken from pajonk's answer.