I have several rat mink and beaver pelts tanned from moyles at least 7 years ago and have just notice after putting back out after Christmas that the pelts are splitting… is there some type of oil I need to put on them to keep them from being so brittle?

Are they splitting all the way through?
I had a coyote and a beaver tanned by some place that was supposed to be good, but the leather disintegrated after a couple of years.
I am guessing due to lack of time in the neutralizing tank and the acid kept on breaking down the fibers.

Possibly due to grease burn in the pelts.
No matter how good a tannery is,grease burn in a pelt can only be remedied to a certain extent.Furthermore if the pelt was stale which is a common cause of grease burn there is not much a commercial tannery can do about it.
De greasing will not rectify grease burn in an old skin,the damage has already been done,but the deterioration may not show up for a while after tanning.
A skin does not have to be old to get grease burnt.Insufficient scraping along with drying in sun,or heat can grease burn a skin
Sometimes grease burn is only in spots and does not affect the entire pelt

This may or may not be the peoblem with your skins,kust one possibility.
Storage of tanned skins in high humidity will also cause leather to deteriorate quickly,Tanned skins should never be stored in plastic bags,or in damp basements.if you store tanned skins in basements over the summer you need to run a de humidifier.

Post pictures will help diagnose the problem

If the pelts are stored or displayed near a heat source - wood stove, furnace - that will dry the leather out faster, causing it to tear.

I’ve got some ranch fox pelts tanned by Moyle in 2007 and stored in a cool place, that are just fine. Almost like freshly tanned.

Is there an oil/product you can work into the leather to prolong them?

Yes a good quality tanning oil watered down will restore suppleness to old dry leather.
I have done that back in the day when re cycling old fur coats.
Furriers will do this when refurbishing or restyling old fur coats.
Dont over do it-less is more.

like said you have to take care of it after you tan it we tanned a deer hide used as a rug had it for years looked good decided to cover heat register with it all the hair fell out our own fault have a lot of tanned fur havnt had any issues sense

shoes are leather like fur what happen to them after you wear them