Yes please, this seems so stupid...
I couldn't find a solution with a GREP style as it apparently can't recognized "lines of text" in order to code : don't apply underline to any space before the end of a line of text (automatic returns not only forced or carriage returns).

This! A million times this! For now, I need to manually not-underline any space that wraps, but as I change the formatting, the space I need to manually switch the formatting for keeps changing. Microsoft Word does this no problem. C'mon inDesign, keep up with the competition! (I flag this as critical as I genuinely cannot think of another problem I'd like fixed.)

Totally want this! This would also be helpful in automated workflows that use variable text. I'd like it to be part of a character style. Like a "smart underline" option in the underline options panel of character styles... could be "Suppress underline for spaces with wrapping text" (last space before wrap not underlined) or additionally, "Suppress underline for spaces" for cases when style only underlines the characters.

Hi-

Hoping that someone was able to provide a solution to this issue?

I am trying to remove the underlined extra space in flowing text that wraps due to variable components upstream in the document

Any advice would be appreciated

I second this request, noting that the marketing group I work with produces thousands of mail pieces annually that have flowing underlined text.
The result is that any text reflow (type size change, text revision, text frame width modified) forces us to have to manually watch for both unintended spaces underlined at end of line and non-underlined spaces that appear mid-text after the text wraps.

Matthew, I can't duplicate what you are showing in the screen shot. Optical Margin Alignment doesn't seem to make a difference. In any case, I think you are raising a broader issue: the lack of intelligent underlining that applies the underline to words or numbers but leaves the spaces and punctuation in the selection untouched.