This site about wedding manners specifically says it is rude to mistake the characters of people's names.
名前を書く際は、旧字体、人名外字などを間違えて失礼とならないように何度もチェックしてください。
Also, if you are willing to accept this as evidence:
人名外字1500V4
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.