Like blocks are still a problem on Instagram if you use dedicated proxies. Your IP is part of a subnet with many other IPs. If there are major spammers on your subnet, Instagram often flags the entire subnet. That means your IP can be effected too (you get the like block) even if you aren't spamming.
It is all about testing many proxies. You must get lucky and find a provider that gives you a bunch of proxies that are on a subnet that has not been flagged (yet). This doesn't mean it won't be flagged in the future. And even if you get some good proxies from a provider, it could be that the next bunch are on a bad subnet.
It used to be much easier, but getting good proxies is much harder now.
Residential proxies are a more expensive alternative. To Instagram it looks like the IP is not on a dedicated proxy, so they are less likely to flag it. Although you are not bulletproof on those proxies either. If you are able to get them, use moderate settings for liking.