How come this county has both Muslim and Christian holdings?

Solution 1:

This is not a bug. Barony level holdings can be owned by anyone- not necessarily someone who swears fealty to the holder of that county. Baronies held other realms are indicated by a small symbol for that realm appearing in the county.

There are several ways this can happen- usually involving taking the county while the holdings are occupied by someone else. Without knowing more about the situation I can't say for sure what happened.

If there are holdings in your counties which do not swear fealty to you or your vassals, you can use the County Claim casus belli to claim them- this is similar to a De Jure claim but on a smaller scale.