At this point, definitely marriage counseling. You guys have entered a rut in which you act like the parent because he can't be trusted to handle his money, and so he rebels, which is what all right-thinking kids do when they reach a certain age. You need to break that pattern before you can move forward.
I would also suggest you look closely for your own contribution to this problem, because the only way to break habits is to change the way you react (as you don't control someone else). Example: you knew he was spendy when you married him, right? So part of the current issue is your belief/presumption that he would change his ways after marriage. This is a common view among frugal people, btw -- what you are doing seems so logical and right that it is inconceivable that someone else, once exposed to the rightness of that path, would not immediately see the light and jump on board. Example: you guys agreed to a proportional split of the bills, but you still criticize him for how he spends the rest of his money. WTF? The whole point of the proportional split was so he would pay his fair share, right? So if he pays that share, why is it your business to control what he does with the rest? Sure, you lent him money, and you have every right to be angry if he is going to spend more before paying you back, but the fix for that is just not to lend him money -- not to lend him money and kvetch about how he manages the payoff.
The fundamental issue here is that he has a very specific view of what money is for, and you have a very different one -- and you both believe your view is right. But the reality is that neither of you is "right" -- there is no such thing as an objective "right." The first step to moving past your impasse is to acknowledge that both of you are grown-ass adults, and you both have equal rights to spend your money however you see fit. Your job as a couple is to figure out how to make sure you meet your responsibilities to each other and to the baby, while still getting each of you as much of what you want as you can manage.
I am going to say that again, because it was hard as hell for me, and so I am going to assume it is equally hard for you: you are not "right," and he is not "wrong." You are both equal adults, with an equal right and ability to make your own financial decisions.
So: if you approach it from that angle, can you see why he is angry and frustrated? Everything you say, everything you do, is telling him that he is wrong, and that he needs to give up everything that he wants to meet your approval -- and then even when he tries to meet you partway, you jump on him. How would you respond in that situation? How would you feel if every time you deposited something in savings, he was berating you because you could be using it for XYZ?
The way you get through this is to stop talking logic. Yes, btw, you are 100% right that he is being stupid and immature and consumerist -- I am actually 100% on your side here. But you have to completely ignore that if you want to make progress. He is being stupid with his money not because he doesn't know any better, but because it meets some kind of emotional need. And you are saving and being frugal because it meets some kind of emotional need. So what are those needs on both sides? Sit down with a bottle of wine -- or a few, over several weeks -- and start talking about all your hopes and fears. Ask him how he feels when he buys a $300 pair of shoes. Like it or not, our society places a lot of pressure on men to be the breadwinner and earn a lot of money. Yes, it is stupid and sexist and retrograde -- but if he feels "less than" because he only makes $30K, it's still very real to him, and so it is a "real" need of his that you guys together have to learn how to meet. What he is hearing from you now is that his feelings are stupid and not worth anything. What he needs to hear is that you value him, and it's important that he be happy, and you want to figure out some way for him to get as much of what he needs as you guys can afford.
Please also note that this is the beginning of the discussion, not the end of it. The end goal is for him to realize that all that consumerist stuff is bullshit, and that the welfare of his wife and itty bitty baby is the most important thing, and that he'd rather have freedom and time with you guys than all the "stuff" in the world. But you are not the one who can convince him of that -- he has to see it for himself. And he can't do that while you guys are so locked into your positions, feeling defensive and attacked. If you open up about your own fears -- fear of poverty, maybe? Feel of that insecurity of what happens if the job goes away, or if there isn't enough money in the account to cover a medical bill, or whatever -- then your vulnerability can help him let his guard down, so that he then can be strong for you instead of strong against you. And once you guys have learned to let your guard down and talk fears and insecurities, you can also talk hopes and dreams -- spending time together, spending time with the kid(s), not working your whole life, ditching it all to travel in a van -- whatever it is that you guys dream of, what you're working for.
Only at this point can you start talking numbers. This is when you can look at where your money is going, and whether those purchases are taking you closer to your big goals or further away from them. And then you negotiate how much you can both put toward current wants and how much should be dedicated towards future wants.
Good luck. You have a hard road here, but it can be done if both of you are willing.
(Also, please note that if he were posting here I would be ripping him a complete new asshole, because IMO he is being ridiculous and immature and stupid and all sorts of "horrible spouse." But he isn't writing in -- you are. And telling you that he's being stupid only doubles down on where you are now -- the lesson for you is to try to figure out how to move past that and hear the "why" behind the stupidity.).