Why did Marvolo Gaunt think that Bob Ogden was Muggle-Born?

Question

In The Half-Blood Prince, Harry Potter and Albus Dumbledore take 'a trip down Bob Ogden's memory lane'. Bob comes up to the Giants door, 'wearing the strange assortment of clothes so often chosen by inexperienced wizards trying to look like Muggles'.

Morfin Gaunt drops out of a tree, and starts speaking in Parseltounge. Marvolo comes outside, asks Bob if he's Muggle-Born, and says that he has the same nose as people in the village:

"Are you pure-blood?" he asked, suddenly aggressive.

...

...and muttered, in what was clearly supposed to be an offensive tone, "Now I come to think of it, I've seen noses like yours down in the village."

My question is, wouldn't Bob's clothes have given a hint that he was pure blood, or at least brought up with wizards?

Or, if he WAS Muggle-born, then why didn't he dress like a Muggle?

Answer 1

• As discussed here in detail, JKR explicitly modeled blood purity sentiments on Nazi Germany specifically and antisemitism in general.

• " I've seen noses like yours" is a pretty dead give-away as to what that whole exchange's point was - Jewish "identification" via a large nose is a common stereotype

• It is a common trait for a bigoted person to accuse the person they don't like (say, a government agent interfering with their criminal activity?) of being the target of their bigotry, very frequently a Jew. The last and most famous episode was from this year, but I observed it pretty much daily growing in Russia.

So, TL;DR - JKR was being anvilitious.

To answer the specific questions being asked by OP:

Q: wouldn't Bob's clothes have given a hint that he was pure blood, or at least brought up with wizards? Or, if he WAS Muggle-born, then why didn't he dress like a Muggle?

A: It is irrelevant to Gaunt whether Ogden was or wasn't a muggle-born or how he dressed. He's suspected of being a Muggle-born because he's disliked by Gaunt, and not because of some specifics of dress.

Answer 2

^{To complement DVK's answer, I would like to add...}

"Are you pure-blood?" he asked, suddenly aggressive.

Are you pure-blood, he asked.

There's a difference between being:

• muggle born and thus naturally aware of what muggles dress and act like, and
• not being pure blood (eg. all of your ancestors are card-carrying magicians).

For example, Harry wasn't "pure blood", but he wasn't muggle born either. The number of people who can truly claim to be pure blood is vanishingly small. As Ron says in Chamber of Secrets:

Dirty blood, see. Common blood. It’s mad. Most wizards these days are half- blood anyway. If we hadn’t married Muggles we’d’ve died out.

Gaunt wasn't necessarily suggesting Ogden's parents hadn't been a witch and a wizard, but that overall he had a bit more muggle in him than a wizard should have (which, according to Gaunt, is none).

Answer 3

It is Marvolo, not Morphin who asked Bob Ogden about his blood status. I think Morphin says something like "you are not welcome here" in Parseltongue.

There is no direct explanation but I think the question has nothing to do with the clothes of Ogden or how does he look like.

Marvolo judges people by their blood status. That's the first (and most of the time the only) thing he is interested about when he meets someone new.

So it is very natural for him to ask such a question.