I can’t really speak for what it is like in Europe, but there’s basically three big buckets that US Christian religion falls into.

• Catholic, was (might still be) the plurality of Christians in the US. Not terribly different than the European version. Some may focus a bit more on different points, but the high level is the same. Gay is a sin, no birth control, male priests only, drinking is acceptable, forgiveness tends to be prominent.
• Protestant, this would be the Baptists, Lutherans, Methodists, Episcopalians, etc. The only thing they really have in common is that they are Catholic BUT one or two major differences. It depends on the specific organization, some take more hard line approaches, some are far more accepting. National bodies are a bit more loose than Catholicism, but still consistent. There’s a mix of reasonable and crazy people in this bucket.
• Evangelicals are the totally unhinged group. Churches in this group are non-denominational, though some may have started as a Protestant sect. They may have loose ties to other churches, or be a mega church. While there is variation here as well, it tends in the more extreme direction. Biblical interpretation tends towards the more literal and cherry picked stories instead of the relative interpretation that traditional branches have reformed to use. Grift is super common in this section. Condemnation of non followers is also common instead of outreach and forgiveness. Young earth creationism is a common belief. This group started growing rapidly with the advent of televangelism in the 70s.

There are a bunch of what are called “mainline” Protestant denominations in the US, which typically includes Lutherans, Methodists, Church of Christ, and by tradition Episcopalians (among others). These churches are part of a larger denominational heirarchy that provides them support but also sets bounds on their doctrine or behavior.

Evangelical churches are typically one-offs with no greater body of faith to report to, reducing accountability and oversight, and often no overhead organization providing funding, meaning they need to constantly raise money to be financially solvent. They also typically have a greater emphasis on evangelism, because they need to constantly recruit to maintain numbers, hence the name.

Mainline churches display a gradient of attitudes on social issues, from very progressive (United Church of Christ) to the very conservative (one of the Lutheran synods) but typically a church professing that denomination will fall into the same stripe as other churches in the denomination.

Evangelical churches are all over the place, though typically radical in some way. Most are very strict on sexual purity, but other than that it’s hard to predict. Some have women in leadership roles, some only allow men to preach. Some reinforce class heirarchies and some sel to abolish them. Some prioritize good stewardship if the earth and her creatures, some advocate dominion over it. Without a greater structure, it often comes down to the priorities of the founding members of that specific congregation.

Now to compare with the Roman Catholic church in the US. The RCC seems to vary somewhat from archdiocese to archdiocese with some leaning more progressive than others. When they do lean more progressive, it tends to be in areas like economic justice, ecological protection, and defense of immigrants (who make up a lot of the RCC in the US these days). They are still very backwards on anything related to sexism, misogyny, and reproductive health.

It’s like anything else, for every annoying or pushy christian you hear about there’s dozens of others doing their thing and not bothering anyone.

And it varies church to church too, with some really wanting to get out into the community and others keeping to themselves but welcoming people who are curious when they come to them.

All orginized religion is a control tool left lying around for con men to abuse to break our societies.

There are definitely temperate Christians in the US and it could be the majority(depending on region), but they are not the loudest groups usually.

The protestants in Urk and the Dutch Bible Belt are definitely not more progressive than the Catholics.

As a very liberal and active European Protestant, I would add that, unfortunately, American evangelicalism exerts a strong influence on European Protestantism. The Lutheran Church of Latvia, for example, decided a few years ago to stop ordaining women pastors. In my (French) church, new pastors are on average more conservative than their predecessors (but the remaining liberal pastors are even more so than their predecessors). Evangelicals have the resources and use them extensively; they are winning the cultural battle, unfortunately. Protestant churches are still resisting, but we will have to learn to make ourselves heard if we don’t want sectarianism to set us back a century or two.

US Evangelicals at this point are one big core group with specific branding and associations that uses the mass of people that go to their churches as a financial and political machine, which their leadership wields to their personal benefit. Anyone outside of the mega-church group are marginalized, with some smaller churches on the fringes.

With the larger group and brand, the Bible means nothing beyond cherry-picking verses to make any point you want. No learning is needed, and everything is how you feel (how the Spirit moves you!) as long as it agrees with what the church says and you tithe. These people would appear as downright heretics to any Christian from the 1800s or before, and have more in common with the Pharisees that Jesus went to Old Timey Israel to call out for being dicks than Jesus himself. Prosperity Gospel, the idea that Jesus gives one money and power if they want it bad enough (entirely heretical), is a big deal for American Evangelicals, as is making a big show of sermons and prayer, something Jesus said was wrong.

It’s entirely about money and politics, selling books and media, making people feel like they belong, and wrapping people and their families up in the brand, making other denominations out to be not even Christian, so if you leave the church you’re abandoned. I’ve had Evangelicals tell me that Catholics and Orthodox denominations aren’t Christian at all, and that the Pope has Satanic symbols on his hat. Seriously. Conspiracy theories abound and nothing is done to discourage them, which is why the Evangelicals won’t turn away Creationist types, but typically don’t confirm that either way. Very little is actually pinned down in terms of religious beliefs, unless it’s something that is a political policy matter.

Since everything comes down to national-level politics and the whims of your local pastor, who often has a high school education at best, sermons can swing wildly around any topic, contradict each other, and provide zero real insight about the Bible or their religion. They’re entertainment the same way that Fox News is opinion-entertainment (so says Fox News in court documents to avoid lawsuits). Leaving space for people with mental health issues, corruption, schemers, idiots, and general human slime to prey upon the church. And it’s a constant parade of those types, pushing people to go out and say and do anything they feel like, and which usually pushes along the financial and political machine.

The Evangelicals in the US are a rather crazy, radical bunch in comparison to Roman Catholics here in Europe. And while Catholics here are more conservative than Protestants here, they are rather civilized. In many European countries the members of the Catholic are more liberal than the leadership in Rome, and there is a lot of stress between the common people and the leadership, mainly to open up as much as the Protestants already have.