Rude to let baby CIO in apt?

So my husband and I have a 6 month old, who is really attached. We could be sitting on the same couch or in the same room, and if she is not being held she will cry. I can't cook dinner in the kitchen, clean the apt, use the bathroom, shower or comb my hair with her sitting right in front of me. I'm fed up with not being able to get anything done. So we decided to gradually let her cry it out. We tried before and failed. She literally cried for 3 hours non stop until we picked her up. We want to try the CIO method, but the problem is we live in an apt complex with really thin walls. Like I can hear my neighbors conversations, hear when they take a shower/use the bathroom, cough/sneeze etc lol I know it'll take time for my lo to adjust and she will scream her lungs out. Is it rude to my neighbors to let my lo cry excessively? Especially knowing how thin our walls are.