I often will peruse the album reviews to get a sense of which album to buy or to see how others rate an album I like or dislike and I find that the word "twee" appears rather often.
And from what I can tell it seems to be a British colloquialism of some sort that is used in a derogatory fashion to denote that something is too effeminate or naively-sentimental or something.
The word twee seems pops up a lot in Genesis album reviews and also in reference to Jon Anderson's lyrics, denoting that the tunes are less than manly or something--as if the reveiwer is saying, "This isn't the progressive rock that would have inspired our ancestors to colonize India, by jove!"
It seems odd that there are prog music fans that get hung up on whether or not the prog rock they're listening to is excessively "twee."
Seems more like the listener's personal problem. But hey, that's just me.