Speaking as someone who is frequently a Token Jew, my opinion: if you say "Merry Christmas", I take it in the spirit it's intended, which is generally "I have a holiday that makes me happy and I want you to be happy" but is sometimes (very rarely) "Burn in hell you unsaved bastard".
I often say "Happy Holiday" or sometimes "Merry Whatever" because I have no particular investment in Christmas and Hanukkah isn't really a very important holiday. However, with someone who I know to be celebrating Christmas I will say "Have a nice Christmas" because I know they will be having a Christmas and I want them to have a nice one. I appreciate the similar effort when people wish me a happy Hanukkah even though as I said Hanukkah is not very important and is already over, because it means they put some thought into well-wishing towards me specifically even if they are not well informed about my religion.
"Happy Holidays" to a mixed group is reasonable but I don't find "Happy (insert thing the greeter celebrates here)" objectionable. The only things that offend me in this regard are:
(A) when someone says "I know you're Jewish, but try to have a merry Christmas anyway" because that sort of underlines the potential "Burn in hell" aspect, or
(B) when it's a card or decoration that says "Happy Holidays" or something similarly generic and inoffensive and avoids mentioning Christmas BUT has a Christmas tree, angels, holly, Santa, a reindeer, etc. etc. I don't know why, but that just really rubs me the wrong way. I guess it's the insincerity of having a deliberately nonspecific slogan with extremely specific graphics.