Woke used to mean enlightened and progressive, but now it is generally used as a derogatory term which means you follow an extreme hard left party line and are intolerant and defamatory towards anyone who disagrees with you.
Woke people are sometimes extremely bigoted, for example they often go straight to ad hominem attacks, calling those who disagree with them bigots, phobic, Nazis and far right, instead of just allowing others the right to have dissenting opinions.
Sometimes the woke will claim that others are causing harm by using words they disagree with and try to shut other opinions and beliefs down. The term woke is now often associated with censorship and thought policing.
As a result there is now quite a bit of pushback on the idea of being woke and it's generally used as an insult as in "Go woke go broke".
Your friend may be a lovely person and great parent who just finds men kissing uncomfortable for any reason. Simply not wishing to watch any sexual act on TV no matter who is doing it is not actually wrong or bigoted. Not wanting to watch same sex kissing or have your child watch it might be that she just doesn't want to try to discuss sexuality and same sex attraction with a young child.
But if the underlying reason is that she feels same sex attraction is wrong, deviant, perverse or (insert other slur or negative) then yes she is prejudiced against homosexual people, and I wouldn't be friends with someone who was a homophobe.
Of course, she is entitled to hold bigoted beliefs as well, providing she's not breaking any laws.
Of course, you cannot know what her reasons are without delving further which might lead to uncomfortable conversations or arguments.
Personally, I have had throughout my life friends who are left and right and centrist, but I am absolutely fine with agreeing to disagree with most things provided they don't harm me or mine personally. I don't see bigotry and phobia around every corner, nor do I automatically make assumptions about other people's reasons for having different opinions. I can have a calm rational discussion with someone from another opposing viewpoint too and they can see that I am not being snide, condescending or consider myself better than them, which has been useful in past discussions.
An example, I was friends with a Christian who truly believed homosexuality was a sin. They didn't hate homosexuals or want to hurt them, but believed if they acted on their feelings they would go to hell. I disagreed, and after a couple of calm discussions, we agreed to disagree. They didn't bring it up in public, or bible thump about it. I haven't seen them in years, but I know they were not hateful or harmful, just (in my opinion) misguided on that topic.
I understand that you will never win hearts and minds by screaming abuse at people, and being abusively insulting to those you disagree with just further hardens their heart and entrenches their position.
However, I would find this a bit uncomfortable without knowing her reasons. If she is anti same sex attraction that will be a problem if her child or other family members turn out to be gay, or have gay friends in the future.
Anyway, there are too many variables from the child's age to your friend's intentions to discuss this reasonably.
I guess it depends how much you want to get involved in this discussion and how deep you want to delve.
As I get older I tend to avoid hanging with people who have very different beliefs to mine as I just haven't the bandwidth anymore, only you can decide if you can be bothered to go deeper.