We are having a baby boy soon, whom we have decided to name [name_m]Harry[/name_m]. Friends of ours have recently had a baby girl named [name_f]Harriet[/name_f]. We had chosen [name_m]Harry[/name_m] a few months before [name_f]Harriet[/name_f] was born, and although these friends didn’t know the name we had chosen, they did know that we had settled on a name. It just so happens they chose something similar. While it doesn’t bother me in the slightest, would you be offended if you were [name_f]Harriet[/name_f]'s parents and we didn’t ask your opinion on whether the names were too close? These children won’t go to the same schools and won’t have a huge overlap in social outings.
I wouldn’t be offended. If you’re feeling uneasy about it though I would casually mention it in conversation, making sure to say something like "you know we settled on a name for our little one x months ago and we chose “[name_m]Harry[/name_m]”. Pay attention to your friend’s reaction and gracefully go from there. Your friend might be excited that the names are a tiny bit similar especially since they are different genders 
I see why you would be concerned, but it’s not like they put a patent on all names similar to [name_f]Harriet[/name_f] when they had their daughter. Asking them for permission is a purely polite move, and if that would help you clear your conscious, then do it. Otherwise, I don’t think you should feel obligated to drop the name you love if they have an adverse reaction to it just because the name they picked has a similar sound.
Good Question OP! You are very considerate. My first reaction is No - for all the reasons you mention. But I doubt you would raise the question if you were not concerned that you might upset her. Many would not worry. PP’s suggestion of putting it out there is good.
You are not going to change your choice - Right? (Sorry edited to add I mean consider changing it because of the circumstances- it sounded a bit brusque) - but by reminding your friend it may help her deal with any negative feelings before your little boy is here.
In my area [name_m]Harry[/name_m]-girl and boy variations are fairly popular in general. There is no obligation I think, so its a lot about your relationship.You are the best judge here and I hope that she will feel positive about it particularly since they won’t be in the same class or such.
No, and I don’t think any reasonable person would be upset.