These amendments weren't something shoved in to get support, they got forced in by a minority of hardline nutcases who have vastly disproportionate power because the GOP majority in the House is so narrow - if the 8 nutjobs that make up the MTG wing decided to boycott proceedings in protest, the Dems would have the ability to dethrone McCarthy and put in a Dem Speaker. Note that four Republicans voted against the revised bill, and four Democrats voted for it (presumably because having it outright fail would be Bad).
This bill now proceeds to the Senate, and the Senate does not have to just do an up or down vote on what the House gives them. They can alter the bill as much as they want, it just doesn't go to the President until after both houses of Congress have passed the same version. More importantly, a bill that comes from the Senate, even one that originated in the House, is not vulnerable to the same sort of procedural shenanigans that a bill originating in the House is. Forcing a simple up-down vote on the Senate version is trivial, and an otherwise identical bill without MTG's amendments will be very popular on both sides of the aisle. Note that the Senate is not only Dem majority (if only just), a fair chunk of the GOP senators are from the wing of the party that isn't deeply invested in the Culture War (which is an explicit reason why Senate terms are so long - insulation from random political fads) and aren't likely to want to jeopardize the military in order to please the nutty obsession of the week.
What's going to happen is that the bill will go to the Senate, all of the stupid amendments will get stripped out, then it will go back to the House and get rubberstamped in the Senate form.