I also use an email alias service and have dealt with this a handful of times. Here's how I've been able to address most of them, in order of what I tried which worked, meaning that items lower on the list were more rarely required but also more likely to work than items higher on the list:

1. Instead of using the free-tier alias domain names (like freealiasservice.com), I used the paid-tier ones (like paidaliasservice.com).
2. Instead of the common domain names shared by everyone (like aliasservice.com), I used a custom subdomain, (like cricket.aliasservice.com).
3. Instead of either of the above, I used a custom domain name.

So the above is the answer to your first question. The answer to your second is that in my experience the majority of sites that block certain email domains are using a deny-list instead of an allow-list. The answer to your third is that custom domains should work for the vast majority of sites. I think it would be silly for sites to use allow-lists for this, but I've heard of some doing it.

One other thing to keep in mind about my list is that it's also more or less in order of most private/anonymous to least private/anonymous. Item 1 hides you in the crowd, while 2 and 3 can be more easy to associate with you if you have enough of them for someone interested in finding this out to do some matching to determine if you use services a, b, and c, for example.

I hope this helps.