Yup. But neither illegal, nor terribly frowned upon by men, who are mostly happy if the tactic results in a greater-than-normal influx of female patrons.
Sexism, in practice, is a highly subjective issue… Sexism where men are the object-victims generally needs to really "raise the bar" before the average man will care – after all, protesting ladies' night is more likely to eliminate such an event, rather than secure any sort of "guys' night" equivalent – the net result being fewer women at the bar/club.
You could also argue a sexist angle in which women are suffering from the benefit of ladies' night, since it basically urges conformity to a dynamic wherein women "pay admittance with their bodies", which commodifies them on some level. I'm not sure many men would be sympathetic to that argument, however.
As to the point about drink specials – I refuse to accept any argument that reducing or increasing the price of an alcoholic beverage in any way removes an individual's responsibility to monitor and pace their own drinking, or that such variable pricing has a direct relationship or responsibility to non-consensual drunken sex play. If that were true, CostCo would be the booze-rape capital of the world.
Interestingly, in at least some places where such objections have been lodged, I have seen/heard of clubs that have replaced their ladies' night with "miniskirt night", or "heels night", and happily admit men for free who are willing to wear the appropriate attire. To me, this is a win on a number of levels, since any man who wishes free entrance will, at least in some small way, have a greater understanding of the objectification of women in modern western society.