Karites were always very tiny. I'm not sure there were ever more than 50,000 of them.
You bet. Of course the Orthodox don't have to concern themselves with them since they don't consider them Jewish. All because the main point of disagreement was whether or not you can light fire on Shabbat.
Long ago, the Karaites decided that lighting a fire before Shabbot to be used during Shabbat was just as bad as lighting a fire during Shabbot. This led to Karaites sitting in the dark on Shabbat and Rabbinicals making fun of them from behind their Shabbat candles.
Later, the Orthodox Rabbinicals decided to that electricity was really fire. Today the Karaites can turn on a light on Shabbat and drive a car because they do not consider electricity to be fire. They make fun of Rabbinicals walking to the Synagogue on Shabbat. The role reversal is fascinating.
My wife is Karaite, and she often tells me of her arguments with Rabbis and teachers growing up when they told here she wasn't really Jewish, but was in fact a Christian! She used to argue with them about the Torah, and how some Rabbinical beliefs are not quite as sound as you might think, such as : why can't you eat chicken with cheese? The Torah only says "Do not bathe a kid in it's mother's milk", which means that kashroot only really requires the separation of dairy and beef, not all meat. All Rabbis will agree with this and then argue that you should continue to separate chicken from dairy because its tradition and Rabbis decided it long ago, even though it is completely unsupported by Torah.
Karaites only believe in the Torah, and do not believe in the many interpretations of the Torah made by Rabbis since the split thousands of years ago. That is why Rabbinicals don't like them, because it's hard to argue that Rabbis should be believed over the Torah itself. Thus the name calling and the teaching that Karaites are "not really Jews"
Anyway, it's nice to see someone out there knows about the Karaietes.