Edit: downvoted for asking a question?
It's standard practice to tack lots of little x things onto the bill because they wouldn't ever really pass on their own, but people don't want to deal with a shutdown to stop them. Sometimes that is a big enough issue that people will deal with a shutdown.
Keep in mind that the shutdown began during the previous congress, when Republicans controlled the House, Senate, and the Presidency. It has extended to the current congress where the Democrats now control the house.
To break down some additional bits and pieces for folks about how the US government works:
A bill (such as a budget) needs to be passed by both the House of Congress and by the Senate and also approved by the President.
Senate rules make it possible to infinitely delay (effectively block) any bill without support of 60% of the Senate (so even a bill that would pass the Senate may not even be voted on if more than 40% of the Senate opposes it).
If the President vetos (doesn't sign) a bill the house and senate can only override that with a 2/3 majority vote in both.
A question to American posters: could any party holding any of the branches of government unilaterally shut down the entire government if they chose, until the next scheduled congressional or presidential election?
Either the executive or legislative branch could though.
The executive makes a budget, but it's just advisory. Officially the House is the source of the budget, which gets passed by the senate, then signed by the president. But as a practical matter there's much negotiation before and during the whole process, of course.
Most of the newspapers don't go into the reasoning behind it and just blame everything on Trump and it's hard to read a one sided point of view of wikipedia, I wanted to hear different opinions on the topic.