When you parallel batteries, the combined reliability generally becomes less than the least reliable battery. In reliability engineering, this follows the equation:
$$R_S=R_1*R_2*R_3 \tag 1$$
where $R_1, R_2,R_3$ is the reliability of the respective individual batteries.
The older batteries are inherently more unreliable. Battery failure modes can cause the charging system to not properly charge the individual batteries and it can reduce the available energy when a load demand is asserted.
The only failure mode that does not reduce the system reliability is a failure to an open condition. This is rarely seen on secondary batteries except when they contain integrated charge controllers, which is not the case for typical lead acid type batteries.
To exemplify the formula, imagine that the new battery is 95% reliable and that the old batteries are 50% reliable. The combined reliability is 0.95*0.5*0.5 or 23.8% compared to 95% for the new battery alone.
Aside from failures of the individual batteries, you may find that your charge controller is either not equipped to handle the combined charge current or it will not properly detect a charged condition of the combined batteries.
If you wish to make your system redundant, at least from the battery perspective, you need to design the system to reliably charge each battery and also allow for each battery to independently supply the load regardless of the state of the other batteries. The reliabilty of a such a redundant system is:
$$R_P=1-\frac{1}{\frac{1}{U_1}+\frac{1}{U_2}+\frac{1}{U_3}} \tag 2$$
where $U_1, U_2, U_3$ is the respective unreliability of each battery. Unreliability is defined as 1 minus reliability.
Using the same individual reliabilities from earlier, this would result in a combined battery reliability of ~96% - not really worth the effort given the marginal improvement over the 95% reliability of the new battery.
If you are relying on this battery system for any critical function, I would recommend against combining the batteries.