Hi there.
We are collecting emails through our SEO sites that are about the topic "how to make money online". We're also writing about cryptocurrencies, which non of the big providers seem to be happy about.
Regular ESPs like activecampaigns and aweber, does not really allow us to send the kind of emails we would like.
We are looking for a tool that can help with automation.
What ESP do you recommend for this?
Check getresponse, they are kinda affiliate friendly and less strict than the two you mentioned.
I also tagged Manu in this thread, he has recently change the provider for their newsletter, so he might have more info on the subject 
ActiveCampaign is one of the most easy-going ESPs usually... Are you very aggressive and essentially get flagged non-stop by spam filters?
Because the topic is generally one to generate that, so if you don't write emails in non-spammy way, you hurt the ESP's reputation. So in the end, none will accept you.
Someone suggested me to check out https://sendy.co/ with Amazon's SES, which is very cheap to use but I'm not certain about all the automation features that you need.
I'd say you need your own setup if you are aggressive. Regular ESPs only work if you don't hurt their IP and domain reputation...
That was quick Manu, did you notice the tag or you found the thread on your own? 
maybe sendgrid should works fine if your list contain fresh/engaged recipients who interested in this stuff
Well, I said specifically that Active Campaign are one of the most easy-going so if they don't let you do it, it's probably best to use your own servers. In other words, there's probably no ESP that you can use... Maybe there's some obscure one built specifically for such offers but I would be worried about deliverability and reliability.
I was using ActiveCampaign for a daily newsletter but switched over a year ago to Campaign Monitor. The reason was unrelated to their AUP though, just about their features for teams.
"Easy going" means that they have a higher than average threshold for spam reports, bounces and such. It doesn't mean they will allow you to sell illegal products, that's just common sense.