Is that yes you can get on? Or yes you can be refused entry?
If that is you can be refused entry, lets look at this your on time to get the train, the guard is at the back door (1st class) of a Pendo and your walking along the platform towards second class the lights start to flash do you run to the standard class to get on, no you just get on at the first door you can (or you miss the train and put a claim in).
Getting on the first class door next to second class at Huddersfield did help to get people off the platform a bit quicker and just walk along the train. On the train the bit that did slow it down was the first class passengers that were walking down the train to first class. Due to the train been formed the wrong way around. Along with passengers looking for the seat that has been reserved for them.
I have stood in the vestibule of first class coaches for years with no problem, I'm not taking up a seat nor trying to get a meal, I don't think that I'll infect a FIRST class passenger with scum bagitus. The bogs are the same as well.
It will be fun on the LNER AZUMAS at coach K stopping passengers getting in the FIRST class door when they have a seat reserved in the second class end (unless that is a coach with no reserved seats).
If a second class passenger is NOT allowed on a train via a first class door of any type then lock out the FIRST class from scum bag class on the train. Then the TTI (old term) can open the door to check the tickets between the classes.