Okay, the simple answer, assuming that you are using the 64bit version of MC26.
Close MC and MC Media Server, if they are running.
Navigate to "C:\Program Files\J River\Media Center 26\Data\Default Resources" using Windows Explorer.
Find the file "Resource.xml" and make a copy of it. Leave the copy in the same directory as above, just in case you have problems or want to revert later.
Edit the "Resource.xml" file with Notepad or similar.
Find the <Entry Key="Space" Command="10000" Param="-1" TranslateFlags="401" /> line in the file.
Edit that line and change it to;
<!-- <Entry Key="Space" Command="10000" Param="-1" TranslateFlags="401" /> -->
The above comments out that line.
Save the change and restart MC.
Test whether the Spacebar still Pauses and Plays media. It shouldn't, but I haven't tested. The TranslateFlags="401" may mean more needs to be done, because 401 is achieved by 256+128+16+1 (refer to green test in "Resource.xml" file), which should mean that spacebar doesn't work in Theatre View. But it does. ? This is why I suspect some Spacebar functionality is hard codes, rather than controlled by the "Resource.xml" file.
Slightly longer version.
Instead of editing the original "Resource.xml" file you can create a new directory "C:\Program Files\J River\Media Center 26\Data\Custom Resources".
Then copy the original "Resource.xml" to the new "Custom Resources", and edit that copy.
MC should use the "Custom Resources" version of the "Resource.xml" file, and hence the Spacebar should no longer Pause and Play media.
Using the "Custom Resources" directory means that future updates won't overwrite the standard (original) "Resource.xml" file, so your fix remains in place. While updates are covered, future upgrades to new major versions will require you to copy the "Custom Resources" directory into the new location for the new MC version. i.e. "C:\Program Files\J River\Media Center 27\Data\Custom Resources".
A search of the forum for "Resource.xml" will find lots of information. A search for "Resource.xml Custom" will narrow the search.