When you widen things up to any form of race or gender recognition, then you have to also realize (which Phantom mentioned), that there is also positive sexism and positive racism. It feels weird to say that, because normally when people say 'racist' or 'sexist', they mean only the negative forms of it, which is understood implicitly from context. If we say any recognition of distinctions is bad, then we create a culture of rigidity and negatively constricting uniformity. This is what 'discrimination' means - treating someone worse based on some arbitrary characteristic. Merely treating someone differently does not equal discrimination.
There are differences between men and women. In my opinion, to ignore those differences is as much a mistake as to mistreat someone for those differences. There are alot of differences between cultures. There are also differences between ethnicities (very minor biological ones), but those differences almost never have legitimate bearing on interactions, unlike gender interactions and cultural interactions.
We should be able to acknowledge someone's race, culture, or gender as long as we're not being offensive. They still might get offended, but that's on them needing to learn how to live in society where everyone has different views and opinions. Those positive views should be expressed, and the negative views shouldn't be expressed unless you know the person personally.
If I'm walking past someone who's wearing a cool shirt, I might say, "Nice shirt!" even to a stranger (in a non-sexual way). If I'm walking past someone with a shirt that I don't like, I'm not going to say "I hate that shirt!", unless I know the person well enough and I'm confident they won't take it badly.
If you know me, and my hair is a mess, and I'm walking out the door into public, you should let me know. There may be a reason behind it ("I didn't have time to shower this morning, I overslept"), but I shouldn't get offended by it because you and I already have a friendship and I know you have my best interests in mind. But if you don't have my best interests in mind when saying it, then you shouldn't say it. Are you informing me for my benefit or for your own?
I can use any judgement I might have to say the things I think will be taken positively, and to not say the things I think won't be taken well. Occasionally I might make a mistake! But then a simple apology should be enough to cover that.
For example, if I see a stranger who's Korean, and we need to interact for some purpose (he approaches me or I approach him for some specific purpose), I might greet them with a typical Korean-language / Korean-culture greeting. This is racism (or "culture-ism" more like). This is giving honor and respect to the differences between our languages and cultures. But! They might not speak Korean, may never have been to Korea, or might even be Japanese(!), and get embarrassed or insulted. Oops, my bad. A simple apology should cover that. If not, that's a problem on their side, and an issue they need to deal with. If we have a continued (non-sexual) relationship, it's on me to respect them as individuals by remembering that they don't speak Korean or are actually not even Asian ().
In actuality, some Japanese or Koreans might get really offended at being mistaken for the other ethnicity (this never actually happened to me, it's just a theoretical example). My mistake is ignorance (lack of knowledge) on my part, but their offense is actually revealing their own racism by viewing the other ethnicity as inferior or viewing them with hatred for past historic wrongs. I'm not liable for their flaws (the hatred/racism), and even though they might get offended that I accidentally revealed it, it's still their problem - exposing what already exists doesn't make its existence my fault.
They shouldn't be any more offended than the two times in the past I was mistaken as a female by strangers - once catcalled at, and another time complimented ("dang, that gal's strong!").
I want to be able to honor people for their individuality as well as for their gender and their culture and other aspects of them as well. I try not to joke about people's culture or gender, only my own culture and gender. If they share my culture/gender and get offended, I should honor their individuality above my joking about our common culture, and refrain from those jokes in their presence.
'Honoring' can even be acknowledging something their gender or culture is weak in. This 'recognizing a weakness' can be taken as an insult very easily, so again, your personal judgement must come into effect, which is easier when you have a (non-sexual / sexual) relationship with the person.
It's super controversial to even suggest that different cultures or genders have moments or areas of weakness. The assumption is that weakness = flaw = me claiming my gender/culture is 'superior', which can be a false assumption. Both genders have their weaknesses and strengths. Failing to recognize the weaknesses and strengths of different cultures and genders creates blindness - blindness to differences is easier, but ultimately worst than, acceptance and recognition of the differences. Equality does not mean identical, it means fairness, balance, and recognition of bringing equivalent value.
Example of recognizing a weakness in females: When someone is in late-stage pregnancy, do you honestly feel you shouldn't offer to help them e.g. carry something heavy? Or after they've given birth, offer to cook a meal for their family so they aren't as pressured to? Using your best judgement to not come off as creepy.
Pregnancy as a whole is not a weakness, but it makes women physically weaker (and, at times, physically stronger), stamina-wise, and brings a large number of other minor or not-so-minor nuisances, even prior to the actual birth.
If someone is old, should you not offer assistance because that'd be biased against young people or because it's acknowledging their present feebleness? They may not want help - but they can easily and politely refuse a genuinely kind offer. To not even make the offer means you are denying them freedom to accept the offer and are deciding for them.
This even applies to entire families. When I was younger, my family as a whole was going through a tough time because one of my siblings was recuperating for several months in the hospital, my dad was working long hours to provide financially, and my mom was extra pressured between visiting the hospital which was almost an hour away, caring for the younger kids (which the older kids helped out with), and cooking meals. Some strangers from our church recognized the weakness and offered to help out with meals for our family - we weren't in too much in need of financial assistance, but we were in need of skilled labor (cooking) assistance, which was provided by strangers who made (correct) assumptions about our needs (I'm actually not sure how they found out - our family doesn't "advertise" our needs, usually being self-sufficient almost to a fault. But word must have gotten around from our close family friends to people we weren't familiar with).
Another example, day-to-day example, of recognizing a gender-related "weakness" is female periods. If I need help on a home-construction project, I ask my competent sisters for a hand. If I realize they are having their period, I try to find someone else to help me before even asking them - and if I can't find help, I inquire if they are capable to help, and based on their decision, might even post-pone my project to a different week if I'm absolutely incapable of getting it done solo.
I must be sexist for thinking of a women's period as a moment of weakness for them.
I must not be sexist for assuming females are capable of being skilled contractors.
I must actually be using judgement on a case-to-case basis, to recognize both strengths and weaknesses, gender-specific or not, in individuals.
Firm hard rules are clumsy substitutions for actual decency and sound judgement. When people lack judgement, they need rules. Guidelines are fine, rules less-so.
To be constrained by super-tight political correctness makes you crippled from being able to offer actual assistance to people who might actually need it. Only when your "offer of assistance" is actually an insult-in-disguise, or when you force your 'assistance' on people who have decided not to accept your original offer, does it become a negative thing.
Even if someone makes a genuinely kind offer based on a stereotype, that's a situation where they need to be taught that the stereotype is wrong; but they shouldn't be criticized for trying to be kind.