My MRes will be unclassified - will this make applications outside academia less competitive?
If you has a 2.2 or for some other reason did not meet the requirements for a position you are interested in, then having a classified MSc would be very helpful. Vary rarely do positions require a 1st. Automated culling of applications based on a 1st or 2.1 generally doesn't happen. Someone will still look at your application if you have a 2.1 and an unclassified MSc. If they see good research, the 2.1 will not matter anymore. 

That said, a student with a 1st is looked at differently then someone with a 2.1. If at the start of the course, you were given the option for a classified or unclassified degree it would make sense for you to choose the classified degree. If you are choosing between equally ranked courses that will both offer you identical learning and research opportunies and one is classified and the other is not, the classified one has the potential to help you more. The benefit, however, is tiny and differences in opportunities, subjects, and/or personal preferences, will offset any benefit between a 2.1 and a 1st.