I've read previously that red text can trigger spam filters.
My challenge is a new client has red #DE0029 in his logo and I want to use that colour for some of the text.
Is this correct, and if so what spam score do filters tend to apply to it?
We've not seen that particular warning before, but there are plenty of odd rules around in different spam filters. We'd suggest just running a few tests to email clients you have on hand, and perhaps a paid design and spam test, to see if it gets picked up.
If you're still concerned after testing, try making your logo an image instead.