I think your premise may be flawed.
You ask about "Christians who reject animals existing >7,000 years ago", but that implies Young Earth Creationists, who reject anything (other than God, of course) existing more than 7,000 years ago.
This means that they also reject any dating of any worldly substance (at least on Earth, but that's a whole other can of worms) which claims an age of more than 7,000 years. So there is no "reconciling" to be done; the Christians you are asking about reject your implied premise.
If you are genuinely curious to learn more, here are a couple places you can go that will start to give you some information on the basis of YEC rejection of Uniformitarian dating:
If you want something with a little more meat, I cannot recommend strongly enough that you read the R.A.T.E. report. You can read a summary here, or download the full report here (fair warning: this is a book; 686 pages long). The second report may also be available. (Personally, I own both in physical form.)