Make suggestions that the item be tabled until the next meeting, that someone call a missing member, that a committee be struck etc. Stop the speaker's list and ask people to speak ONLY if they have something new to say. Make a proposal and test for consensus. Postpone the decision until you have more information or new ideas. Ask everyone else to listen carefully.
Feelings are always valid and real.
Perceptions can be mistaken, however. Listen to what the person is asking for and find out if you can provide that. Ask them to provide suggestions or solutions. Probe the problem until you have a clear understanding of the specifics and can break it down into manageable parts. Often groups have unequal representation.