To think 'not conventionally attractive' means ugly?

It doesn't mean "ugly", no. It means that if someone is so shallow and thoughtless as to judge that beauty/attractiveness only exists on a single scale of hiw closely someone resembles a vanilla hollywood star look (googling top hollywood female actors and the first 3 faces shown are virtually indistinguishable from one another) then the "not conventionally attractive" face does not resemble those and so might be thought "ugly" by someone that shallow. However, there are plenty of other kinds of attractive faces and someone can be attractive in a very unconventional way. I'd expect anyone who uses the phrase "not conventionally attractive" to follow it up with something enthusiastically complimentary e.g "but has the most amazing cheekbones and looks so striking with (insert context) that conventional definitions go out the window..." - if there's no followup compliment like this they can give withoutlying, then using the words "not conventionally attractive" is just rudeness. There is no need for anyone tlo comment on someone else's attractiveness if not to be complimentary.

I can think of many famous people who I see posted on social media as WOW how incredible do they look? and I think, I really don't see what you see. So, you can ugly or stunning.. beauty is in the eye of the beholder. Someone might have said it to mean ugly but it usually is a compliment. Your looks probably divide people and an acquired taste.

I would have said someone who is attractive (probably very attractive) but in an unusual way, not like a Barbie. Think Tilda Swinton or someone like Helena Bonham Carter rather than Gigi Hadid.

Girl next door is not a compliment it means plane jane, small village type of pretty.. 'homely'

If they weren’t using it as a sort of veiled insult, I don’t know why anyone would say this. Why even comment on someone’s attractiveness at all? Especially if you’re going to say something that could do easily be taken badly.

It can be a compliment. It was used about the model Erin O’Connor in her younger days. She was not ‘pretty’ as such, but stunning in an ‘angular’ sort of way, with a great rebellious streak to boot. Def not an insult.

No, I would use it specifically for someone who is attractive, but maybe with features that might not be traditionally considered attractive. For example, my MIL described Alan Rickman as not conventionally attractive and I know she thinks he’s gorgeous!

No I think it means you are attractive just not in the typical Hollywood way.
Ugly is ugly, people don't sugar coat it specially online or children.

I use this for someone I find really attractive but not in a model kind of way, more of an interesting, striking kind of beauty.

The French have an expression “jolie laide” for this. Literally it means “beautiful ugly” and it’s a compliment.

I use it to mean someone is very attractive but not in a model type way, as in, not that sort of girl next door, symmetrical features type way.

It's a good thing!

I think people have used it in the past about Adam Driver for example (and he did a vogue shoot so go figure). I agree with @HangingOver. it implies a different look to the norm, but nevertheless attractive. Otherwise the subject is just “not attractive” surely.

I mainly see it used about male celebrities, and no, I don’t think it means ugly.

The French call it jolie laide and it’s considered a good thing. Oh la la

Yeah, I think it means attractive but not in an obvious model/movie-star way

I always thought this phrase had an implied ellipsis...

Like "not conventionally attractive (but none the less attractive)".

Multiple people use this phrase about my neighbour who is extremely hot

I take it to mean there is something very attractive about someone but they are not stereotypical what we think of as attractive,