gametext:

If you would claim or move power to your house, you must place it on a brotherhood charachter instead. Opponents may choose and take power from your brotherhood charachters to fulfill the claim of Power challenges initiated against you.

Yesterday we played our first games with the brotherhood agenda. The question came up if you could claim power for your house if you don´t have a brotherhood charachter in play.

The first sentence advices you clearly that you "must" place the power on a brotherhood charachter. So if you don´t have a brotherhood charachter in play you might not be able to claim power?! However that´s contrary to the formulation of the second sentence "Opponents may choose ...". If the first sentence would exclude the possibility to claim or move power to your house, i would rather expect a formulation like "Opponents may take..." - without the word "choose".

This agenda effect is a replacement effect. If you don't have Brotherhood character in play it will resolves unsuccessfully.

The word choose is used so that this effect will target the character from whom you take power. So you would not be able to take power from characters that are immune to card effects.

Old Ben said:

The "may" is less about permitting your opponent to take power from a character or not when winning a power challenge as it is about permitting your opponent to choose which character they take the power from.