Alt accounts are fine and permitted by the rules:
18. Having multiple accounts and account sales are allowed, but account sales are discouraged.
Lots of people have known alt accounts and don't get red trust. Lots of very established members have alt accounts. Even theymos has an alt account:
theymos_away. So does global moderator hilariousandco.
People who get red trust on alt accounts are either because they are using multiple alts to break the rules of some bounty campaigns, or because they are a scammer using an alt account to try to evade red trust.
Forum rules clearly say "You can use different accounts". Even this is encouraged.
In this case, it is ethical to participate in signature campaigns on different accounts.
The forum rules are not directly linked to red trust - you will be banned for breaking a forum rule, but you won't be banned for breaking a signature campaign rule. Similarly, there are plenty of things which are not forum rules which you will receive red trust for. There's nothing in the forum rules regarding scamming, and yet it's widely accepted that you will receive red trust for doing so.
Some signature campaigns allow alt accounts and some do not. If you enroll alt accounts in one that does not then you are breaking their rules and liable for red trust. You won't be banned for it, though, because it's not against the forum rules.