Matt:
S&W revolvers have incorporated a safety bar (hammer/firing pin block) for decades, longer than they have had model numbers assigned (such as Model 36). This device requires that the trigger be pulled fully to the rear, releasing the hammer to fall with pressure on the trigger, for the firing pin to pass through the recoil shield and strike the primer.
When the hammer is down and the trigger forward the safety bar stands between the hammer body and the frame within the hammer recess. A simple test of its proper function is to take the (unloaded) revolver, pull the trigger fully, allow the hammer to fall on the (empty) chamber, then release the trigger. You will notice that the hammer rises as the safety bar returns to its position in the frame recess.
There were many demonstrations provided by S&W of the safety of this arrangement years ago. These included (1) placing the loaded revolver in a vise and pounding the hammer until it broke, without discharging the weapon, and (2) cocking the revolver into the single action mode, then striking the trigger with a rod; before the firing pin could strike the primer the safety bar rose to prevent that.
Assuming that your Model 36 is in proper operating condition, and has not been altered from original specifications, it is entirely safe to carry with all five chambers loaded.
That said, in years past, some users were known to remove the safety bar in an attempt to improve double-action trigger pull. As far as I know, this was done primarily by competition shooters. Any improvement in trigger pull was probably minor at best. If you purchased your Model 36 used, a quick inspection by a knowledgeable gunsmith will determine whether any modifications have been done (not a bad idea with any used firearm, actually).