Presidential budgets can matter. Here's the deal. Remember that presidents have few legislative powers. They have the power of the veto, and that's quite a power. They cannot propose amendments, though, and they cannot even introduce legislation into Congress. Their budgets are basically dead on arrival.
What is measurable, though, is that presidential priorities, as determined by the kinds of statements made in presidential speeches, are more likely to be taken up by Congress. Not necessarily passed, but at least worked on, and budgets are statements of priorities.
Donald Trump's budgetary policies are mostly boilerplate Republican policies. He isn't a "conservative," in the Phil Converse sense. Converse defined ideology in terms of "constraint." To be liberal is to be "constrained" to take the liberal positions on a wide range of issues, and to be conservative is to be "constrained" to take the conservative positions on a wide range of issues. To be a true "ideologue" is not just to hold those positions, but to understand the underpinnings of the belief system.
I think "object permanence" might be too advanced a concept for the Very Stable Genius-in-Chief, so expecting him to understand the tenets of conservatism at a philosophical level would be like expecting one of my cats to be able explain the evolutionary development of the predator-prey relationship and how equilibrium is reached in an ecosystem. Mostly, they just whine when they're hungry and look at the birds outside, deluded about their ability to catch such things.
Trump had no real input on the development of the White House budget. It is a boilerplate statement. More military spending, cuts to domestic programs, and... something about infrastructure which you can safely ignore.
For the most part, Trump is not really deviating from conservative orthodoxy. Ignore all the blather about how increasing the deficit is a change for the Republican Party. Deficit hawkery died in the GOP when George H.W. Bush (Mr. Voodoo Economics) made his "no new taxes" pledge, had to back down from it, and then lost in 1992. When Dole ran in 1996, the former deficit hawk ran on a flat tax pledge. Nobody in the GOP has seriously cared about debt or deficits in more than two decades.
No, the Trump budget is Republican orthodoxy, deficit expansion included. He really doesn't deviate from Republican orthodoxy much, and where he does, congressional Republicans don't fight for his policies.
So, um... how's that wall comin'? If the GOP really wanted to fund that fuckin' thing, they'd do it. And Democrats couldn't stop them. Why haven't they? Because if they really did dump billions of dollars of US taxpayer money into a wall that wouldn't even come close to completion, which Trump promised Mexico would fund... it would be a fiasco, and congressional Republicans don't want to be on the hook for it. Sure, they'll push for a few dollars here, and a few dollars there, but they don't really have Trump's back on that.
What's left? The infrastructure thing? It deviates from modern conservative orthodoxy, and it won't go anywhere. It's just Trumpian bluster, and it will be ignored.
This post might give you a different picture of the relationship between congressional Republicans and Trump from what I normally describe. Why? Different politics.
Congressional Republican leaders have zero respect for Donald. They know he's a joke. They have a strategic need to defend him from any and all accusations, but on policy? As long as he adheres to conservative orthodoxy, they're happy to have him sign their bills. Otherwise, he is to be ignored.
This is the most bizarre relationship between a president and congressional leaders I have ever seen. Each side treats the other as useful idiots. When it comes to policy, congressional leaders see the president as the useful idiot. When it comes to legal defense, the president sees congressional leaders as the useful idiots.
And they're all correct.