Keep in mind that there are ethnically Romani, and culturally Romani otherwise known as gypsies. Equating them just based on their ancestry, or comparing an entire ethnic group to the homeless is pretty racist.
I disagree. The assertion isn't that the two groups are the same. It's the mainstream desire to kill them that's the same. Probably, allegedly, maybe...I think so.
Imagine coming up to some educated person with a normal job that looks vaguely like a northern Indian and telling them they're the European equivalent of the homeless in the USA. Or saying something like "black people are the Amerikkkan version of Brazilian favelados".
And I've only seen that desire to kill them with literal Nazis. There are a lot of ways my government is trying to help them break their generational cycle of poverty and suffering. For example in my country universities have separate entrance exams and scholarships for Romani. Hell, it's even pretty much traditional to invite gipsy musicians when celebrating big stuff like weddings and children being born.
It can be, but it's not really. It's just the name for the culture, while Rom/Roma is the name for the ethnicity and literally means human. There's a reason why they popularised phrases like "gypsies also have souls".