I feel like bitching about people using the term "Happy Holidays" is on par with bitching about people who say "Merry Christmas."
The thing is, the latter of these rarely happens. Yes, many stores encourage their employees to say this, not to shit on Christmas and make baby Jesus cry but because you cannot assume everyone is Christian and/or celebrates Christmas, and it's not like you cannot answer back with a holiday greeting of your choosing. In the case of something like the tree, again, it's not trying to piss people off, it's trying to be inclusive. I celebrate Christmas and I'm not religious, as do many others. The tree is a symbol of the festive holiday season, and has nothing to do with Jesus or God or anything. Tree worship isn't exclusively a Christian thing.
People are free to celebrate what they want (or not celebrate, if that's their thing). Nobody's trying to take that away. Including others doesn't lessen your rights. Most people don't care what others choose to say, whether it's Happy Holidays, Merry Christmas, Happy Hannukah, etc. It's not like if you say Merry Christmas to atheists we burn and sizzle with damnation or anything. The only time it gets my goat is when governments and/or public schools favor celebration of a particular religious holiday (e.g. celebrating Christmas only or Hannukah only).