My neighbor said it varies across the country. It’s more traditional. In this area, you are expected to always find a Mormon church rather than visit another church. Evidentally, there is some record keeping involved.
There is no “record keeping” involved. Mormons are free to visit other churches, without any restriction.
The ward clerk keeps track of gross attendance at various meetings, but no one is keeping track of whether any particular individual is attending church meetings.
And, even if they were, that wouldn’t preclude someone from visiting another church if invited.
If you are talking about simply attending a different church if you are visiting somewhere away from home, most Mormons would look for another Mormon church. For us, the purpose of attending Sacrament Meeting on Sunday is to take the sacrament as administered by those with priesthood authority. If a Mormon family knows ahead of time that they are going to be far away from a Mormon meetinghouse, their Bishop can give them permission to have the priesthood holders in the family administer the sacrament. The family would probably hold their own little meeting, then.