Static loading makes any difference for security only in situations where malicious people may alter the files that you load dynamically, at which point it is fair to say that you have bigger troubles at hand.
If we really want to talk about security in relation with static Apache modules, then we might argue the following: non-static modules make third-party packages easier. In, say, a Linux system, you would have a "main" Apache package, and you could have a module provided by another package. For instance, on a recent Ubuntu server, you may have the
apache2-bin package, that provides Apache itself, and
libapache2-mod-php5, that provides the PHP support as a non-static module. The PHP support can be in another package precisely because it is a non-static module.
If a security issue is found in the PHP module, then that package can be fixed (with a new, patched package) right away, without having to replace the Apache main package in any way. Thus, hopefully, the fixing process is faster: less people involved, smaller fixed packages to download... In that sense, non-static modules can be thought of as enhancing security, but that is very indirect. What improves security here is the ability to split the code base into several packages that can be upgraded separately, and non-static modules support that model.
Note that static modules could still be managed as independent packages, but this would require the package manager to recompile (or at least re-link) the Apache binary whenever a static module is upgraded. Recompilation upon upgrade is a viable strategy (that's what the *BSD systems like FreeBSD do with their "ports") but, as a rule, Linux distributions have chosen the "binary packages" path.