You have no idea the lengths people will go to.
If all you wanted to do was test a product out, create a real email address even if it's full of bogus details.
If you won't try my product without a real address then you're a customer I don't want and don't need.
For a product with a "free tier" that doesn't work where a user needs to sign up several times, the product itself is flawed.
However, disposable emails again are not the problem, as there are tons of ways to get valid, working emails to bypass any unique email requirements. Blocking disposable emails aren't going to help you with that. The only thing you're removing it a user's access to better privacy. Again, if you require knowing who your users are then you are not a free service.
If you don't care about having users unless you know their real email addresses then you should consider validating their identity in other means, besides an email address. Many services use a text message to validate you also have a phone number that works, which is much harder to anonymize (although I personally have four different numbers for this very reason, based on the trust I give a service I decide which number I want to provide them - since to me, my privacy is worth something, I don't share it for free).
Two observations.
1. Prioritise paying customers. Use spare provisioned capacity to provide for the free tier: don't spin up new capacity for free tier customers - or at least do it on your own terms. Now it doesn't matter if people milk your free tier unless you believe, almost certainly incorrectly, that these people would pay if they couldn't sign up for more trials.
2. We had repeat signups from gmail accounts, but almost none from disposable addresses as such. Any service that lets you have multiple email addresses for free is a potential "risk". That obviously includes any self-run email server, or any corporate email server from the perspective of a user allowed to add new addresses to their mailbox.
Some users may value your service so much or their privacy so little that they may pay up, but for the rest of us it's back to the disposable email arms race.
PS: Kudos for being open and considerate enough to defend an unpopular position on here, though it's ironic that you did so using a disposable HN account.
Is that what asking for an email to sign in to create an account to use a service that probably doesn't work well without having an account is now, invasion of privacy?
Where do we put our foots down and stop saying that everything a SaaS does is sacrificing the user's privacy... Soon we're gonna start seeing "Whoa, asking them to pay and input their credit card? You're asking for the sacrifice of your user's privacy."
You are well within your rights as a business to decline potential customers over something like this, but you need them more than they need you.