It does sound like the main concern has to do with conversations where there is a person of color involved – to make sure that what you have to say or think you have to say doesn't get made more important than what they say.

One way as an ally to help is to help negotiate for time for others to speak, with phrases like "I'd like to hear what ___ has to say" – if ___ is a person who has been trying to say something and has been talked over by white people in the discussion.

I have also been given the message that sometimes POC would like other white folk to step into a conversation where a white person has pulled it down into Racism 101- to offer to explain the basics yourself rather than continuing a situation where the POC has to do all the explaining in order to be understood. Saying something to the POC in this situation to make sure they'd appreciate assistance, and they you'll cater to their preferences, such as "may I try?" would be the polite thing to do – the point being that you can either complete the 101 discussion faster than the POC, because your fellow white person will listen to you better (sadly)–and then return the conversation to the higher level point the POC was trying to make, or you can take the 101 discussion offline into a personal discussion if it was derailing a discussion the POC was having with others. Either way the point (and hopefully the result) is to enable the POC to better discuss things without getting bogged down in explaining racism 101 and without being accused of taking something too personally that is in fact a systematic truth.

Pumping up the volume – repeating what a POC has said, and supporting it — is also good, as long as you give proper attribution and let them complete what they have to say.