In America, the anti-Romani and anti-immigration stances of many "left" European parties would be considered right wing.

It's almost like not all issues fit neatly on a single left/right dimension.

Also the Democrats created Obamacare which is similar to the Swiss system of mandated insurance, so they obviously do care about healthcare.

And in many states, Democrats have passed gun control at the state level.

> They don't even support having a healthcare system

That doesn't sound right.

> or banning guns.

In which other western country or part of Europe are guns banned?

It isn't right, but also... in the US, parties are institutionally weak. People do not (cannot) vote for parties, but for individual representatives. Ergo, different Democrats (or Republicans) run on issues perceived to have saliency locally. From such a collection of elected individuals, it is much more difficult to craft a "party" position -- because in some districts, supporting healthcare/gun control/whatever is not a winner.

Increasing partisanship and gerrymandering are making this less true, but it is still a significant force, particularly for Senate seats.

Strong parties, that run on a policy platform and where they have much more control over their members, just isn't a thing in the US, and couldn't be, without a lot of constitutional changes.

Not sure about that. Lots of voting systems don't vote for parties directly either. And I would say the two parties in the US are extremely strong, FPTP seems to reenforce that. It might also lead to the parties accepting some level of dissidence from some members -- better for a blue party to have a slightly red-ish congressman in a red state than to cede it to the other party. But I don't think that really weakens the parties because it goes both ways.

Minor parties and coalition governments in other countries function in somewhat the same way. It's not uncommon for a party to win but not gain absolute power in the legislative branch of government, and have to compromise with others to pass laws and spending bills.

> They don't even support having a healthcare system

Democrats are the ones pushing for universal healthcare: https://democrats.org/where-we-stand/party-platform/achievin...

> or banning guns.

Yep, they're the ones pushing for gun control too: https://democrats.org/where-we-stand/party-platform/healing-...