It shouldn't matter how many friends you have, but if that is the case, it is only affecting people with a ton of friends, so your solution will probably be what you need to do, unless you want to slim down your friends list.
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People with less friends than what I have have reported this issue too. I wouldn't consider the amount of Steam friends I have to be that insane. Also, this issue doesn't happen in any other game, even those with built-in friends lists. I shouldn't be required to play in offline mode just because I have higher than normal Steam friend count.