The "Freeze Field" feature does not work the same way when a table join is on the feature class. Normally if I want to freeze a field like the highlighted "NAME" field below, I right-click NAME, select Freeze Field, and it moves over to the left of the attribute table, adding the darker grey bar to show it's frozen.
But I've noticed that if I have another table joined to the first table, then when I try to Freeze Field, it just freezes the first field in the table. In the screenshot below, you can see OBJECTID is frozen, even though I clicked on NAME to freeze.
