Cloudflare and IP blacklist services do not specifically target anonymity networks. What they do is look at the amount of traffic coming from particular IP addresses or ranges of addresses and catalogue how much of it is malicious. They apply blocks based on how malicious a given address appears to be.
VPN providers do not have any particular technique to avoid this. In fact, popular VPN IP addresses often are heavily blocked. The only reason Tor is more likely to be blocked is the fact that, because it is free, each IP address sees significantly more use, including for spam. This results in services like Cloudflare seeing more malicious traffic coming from Tor exits and applying increasingly harsh blocks. It is true that the list of Tor exit addresses is public. This is an unavoidable aspect of the protocol's design. However, that fact is not a significant reason for why Tor relays are blocked more often.
There are entire third party services which collect IP addresses that have been used for malicious purposes and provide such blacklists to their clients either for free or in the form of a subscription. A popular example would be DNSBL, which contains IPs from both many Tor exits and VPNs.