Think of the issue this way: It is up to the individual to decide upon their course of action. A liberal merely defends this right for every one, equally, whether it is Individual A or B, or their mothers or sisters. And there is no hypocrisy in this at all.
So the answer to your question "we agree with your position on this, so how about we pay X amount of dollars so that we become your daughters first customers?" is that the (adult) daughter has the right to decide. And of course the other party can make the same offer to your daughter - to let her decide.
See how that works?
Since we're talking empowerment of women in this thread, lets take your argument in that framework. Now going by your definition, ideally a liberal will defend the ideology of "live and let live".. Except ofcourse when
-Erin Pizzey established the first domestic violence shelter in the modern world, but refused to go by the narrative of the feminists that domestic violence is a one way street where men are abusing women. When she refused and stood for the fact (has been proven through research) that DV is reciprocal. The same liberal feminists, whose mantra is to "live and let live" and "equality for all" were the ones calling in bomb threats to Erin's seminars. Someone shot her pet dog during this period of harassment. She had to live in exile thanks to all this harassment by the very same liberal ideology group that believes in "empowering women" ..
-Let's look at the MRA's a movement for boys and men. Ideally liberals should be respectful of their opinion and let them live ... right ? Except we see fire alarms being pulled on regular basis, violent protests etc. You can view the following video as a proof for that ...
Basically, the "live and let live" mantra is all okay unless ofcourse when someone disagrees with the liberal positions on certain issues, then the gloves are off and everything is fair game ..
As far as the comment about the daughter goes, it was simply put to show that when the same principles are applied to the liberals they don't exactly fare too well, and although it's easy to say that " the daughter has the right to decide" it doesn't exactly go that way and we both know that. In the heat of the moment even prominent progressive liberals loose all their cool and stoop down to the same things that they are against "in theory"
I remember a few days ago, I was on youtube and landed on a video. Now in this video, the popular channel " the young turks" were doing a segment on one of the conventoions. In came Alex Jones from the infowars and he just came in the frame, and although he tried to hijack the show, there was no aggressive physical contact or yelling by him. Well not atleast at the start. I've nothing against these guys (the young turks), in fact I think some of their videos are actually good.
However when the chips were down and it was time to show the liberal values Ana Kasparian who I think also holds a teaching position in a university in addition to her presentation job, well she is very vocal on the issue of fat shaming etc. But when it was time to show those values in a confrontation. All the values went out the door and she calls that guy a "fat f*ck" .. Similarly, the same liberals progressives that talk about freedom of expression, in this case Jimmy dore, goes out his way and spits on Alex.
So the point is while you can point to one generic statement, which not many people would have a problem with -- in practicality "live and let live" is only a myth. It's simply your version of morality versus mine with strong arguments on both sides and when it's clutch time, nothings off limits...