I hear two different questions.
1) What is the max permissible input voltage to the CP5?
2) Can I use a 24V battery charger.
For question 1, no one likes to hear, "it depends". So, the keypad has a max input voltage of 28.0V. This is where the 28V "specsmanship" number, mentioned in the other thread, comes from.
This answer is unsatisfying, so we can be more pragmatic by entertaining question 2 instead of question 1. I think this is really what you are wanting to understand.
A proper three-stage charger can provide up to 29.4V absorption voltage at the max absorption set point. This exceeds the keypad rating. Are you even using a keypad???
If not, the next "limit" is the transient suppression, which can begin conducting at 29.5V. While the margin sounds low, the suppression voltage has a large positive temp coefficient when it begins to conduct, and, there will be losses in the power cable to the CP5 contributing to margin. So, the margin is much higher than it seems. So, if you do not have a keypad plugged in, I see no issue using a battery charger.
Suppose you DO have a keypad. Do you know the absorption set point of the charger? Does the charger even have an absorption set point? If so, do you have control over it? Does it transition from absorption to float properly (does it even have a float stage)? Can you measure the highest charge voltage? If the answers are "no", I would be reluctant to have a keypad plugged in while charging. Reason is, there's just too many crappy chargers out there, with no possibility of us testing every one of them. An absorption voltage set point can be as low as 28.2V. We know that, even with the mount parked, there will be a couple tenths drop in the power to the keypad through two harnesses. *IF* you know the absorption voltage to be at the low end of typical, I see no issue using a charger even with a keypad.
I hope this helps.