This site about wedding manners specifically says it is rude to mistake the characters of people's names.
Also, if you are willing to accept this as evidence:
This is a program and collection of fonts specifically for rare/old kanji names. It costs ￥50000. I don't think they would be able to charge that if no one thought it mattered.
Also, as I said in my comment to Tim's answer
When I worked in Kochi City Hall I saw somebody using a font editor to modify 告 into the character known as つちよし (吉 in which the 士 is 土). I think it was going to be printed on an invitation or something like that so they went through the trouble of manually editing the font.
However, all the information I could find was about weddings, funerals, and invitations to formal events. So, it seems to me that in a general, everyday context 常用漢字 have been acceptable in informal correspondence. But as phones and other devices become able to display more characters, this attitude may change.
That leaves business correspondence. If I had to send an email to someone I knew on a business level only, I would be sure to write their name with the correct character. Where that is not technologically possible, I would use a character that is displayable and ask them about it later.