According to halacha, a man should not walk behind a woman.
According to custom/manners a guy should hold the door open for a woman.
They are contradictory points. If a date is choosing to be makpid – see if it carries through in other areas of tznius (since that is what it’s all about). If he is polite and mannerly in other ways, and is consistent with his hakpados, then you can consider overlooking it. If he is being “fachnyuked” about just this prat, than maybe you/he need to reconsider what his actions mean.