IANAL, made a throwaway account for this post because it pissed me off.
Hi OP. I'm not a lawyer but I wanted to offer some perspective because I am in a similar situation. I bought a house with a good friend a few years ago and my parents loaned us the money, about 625k, to do so.
My parents did well in their respective careers and inherited money from extended family. Someday, like your BF, I will inherit their house and the majority of their money. From that standpoint, I can relate to your BF’s perspective.
My parents offered to lend us the money for a house for probably the same reasons your BF's family did. My good friend was someone who I had already lived with for years and trusted with my life, and neither of us could afford a house on our own.
Friendship aside, we all wanted to have legal documentation in place to make sure everything was on the up and up, and fair for everyone. I was also conscious of the fact that I had the upper hand in the situation since the money came from my parents and I didn't want to unfairly benefit or jeopardize our friendship. It is interesting to me that your BF does not feel the same way. If he valued you as a life partner, why would he be so against protecting your future?
Here's what we did, with a real estate attorney, that I would recommend you do IF you go through with this—which I wouldn't.
We all agreed there was no conflict of interest if the same attorney represented all of us but in your situation I would get your own attorney.
The money was loaned to us at the long-term AFR (Applicable Federal Rate - this comes from the IRS). My parents have an official mortgage document with a lien on the house - if we don't pay, they can foreclose on us. We can make extra principal only payments, or interest only payments if either of us experience 3+ months of financial hardship. Each year we both get a separate 1099 INT so we can deduct our mortgage interest on our taxes. In the eyes of the IRS/law it is an official loan agreement just like it would be if it was through a bank.
While we put down different amounts—I put down 17% and my friend put down 10%—we each own 50% of the house and my parents loaned each of us 50% of the purchase price. I have my own promissory note/mortgage documents for my 50%, and my friend has their own documents for their 50%.

The last thing we did with our attorney was draw up an 8 page ownership agreement to cover as many situations as possible. Not because we didn’t trust one another, but because it is a lot easier to create legal guidelines before a situation happens to remove any opportunities for resentment between us. This covers maintenance, utilities, upgrades, insurance, taxes, and other costs - we each pay 50%. It has a first right of refusal clause - if someone wants to sell their 50%, we have to offer it to the other person first. It covers what happens to our share of the house if either or both of us die, what happens if either fails to pay or files bankruptcy, if we want to rent out part or all of the house, what insurance coverage we have, how we decide on large purchases, among many other things.
Our names are both on the deed because we each own 50% of the house. It's extremely concerning that your boyfriend and his family do not want your name on the deed. That was one of many giant red flags for me. That alone would make me back out, if not reconsider the relationship entirely. If he and his family do not view you as an equal partner/contributor to his life who should be equally valued and fairly compensated, there's something wrong. If his parents only wanted to lend him the money and have you on a lease that would be different. The fact that they dismiss your concerns is not okay.
I really want to stress this part. When my parents loaned us the money, my friend put down less than I did because of our individual financial situations at the time. Regardless, we each own 50% of the house. Our ownership % was not related to our down payment amounts because we all thought it would not be right to enter into an unequal agreement. This was never even a discussion... the only person who ever brought up having unequal equity was the attorney because he saw our different payment amounts.
If you feel like you’re paying for your BF’s house with no financial safety net, it’s because you are. It’s very disingenuous of your BF to present this as a gift to you when it is only a gift to him–from both you and his parents. It’s even worse for him to suggest you’re being unreasonable for having concerns. As the person with the upper hand in this situation, he should have preemptively offered to address any concerns you had before you brought them up.
As the top comments said, you should have a lease if you’re not on the deed of the house. I understand your reservations with that agreement, but it’s the only one that is at all fair to you if you are not on the deed.
I believe that if his parents want to lend you both the money, they can’t do that without putting your name on the deed. Otherwise, there’s no collateral. I could be wrong about this - ask someone more knowledgeable! I also dislike that you would pay more as you make more. That could be fine but given the context of the post it sounds… fishy. Would your BF have to do the same?
To be honest, I would run from this agreement (and the relationship). I don’t like how your BF is treating you, talking down to you, and ignoring your very realistic concerns. I also dislike how his parents are approaching this. Yes, it is their money to use as they see fit, but it seems like are approaching this with a controlling mindset and they don’t value you as they should. If they did, they would have offered a fair arrangement from the start and asked for your input.
The other thing my parents did was to write my friend and I each a check for $5,000 because they “know how hard it is to get started in life” and wanted to “use what they had to help us as much as they could and prevent us from worrying about any big upfront expenses”. I truly hope this doesn’t come off the wrong way. I use that example to illustrate the difference in mindset because it sounds like your BF’s parents don’t want to genuinely help you both, they want to control you/the money/the situation.
Again, I don’t want this to come off the wrong way. I wanted to offer some perspective that might help you consider the position and relationship you’re in. I know I am beyond insanely privileged & lucky to be in this situation and I don’t say any of this to brag about myself. My parents were also privileged and lucky and are generous to a fault.
Feel free to ask any questions, I’ll answer to the best of my abilities.