It seems like some oil changing stores do not use a Mobil 1 oil filter even if they use Mobil 1 engine oil. When using Mobil 1 engine oil, is it much better to use a Mobil 1 oil filter?
No, but using a quality part for your engine is. Some “cheap” filters may not have the performance or longevity of a quality filter.
Really, a “cheap” filter is poor economy considering the function of the filter and the cost of an engine.
This applies to fuel filters as well.
Use a quality brand - there are several...