You definitely don't want to mount a long metal pole through a Yagi. My rule of thumb is that it at best cuts off the Yagi at that point, perhaps worse.
You have three options to avoid this.
Mount the Yagi at its back, perhaps supporting the front with a non-conductive rope. The mast can get quite close to the reflector, 1/8 wave is ok.
Offset it from the mast with a bracket that's perpendicular to the plane of the Yagi. Exact length required is hard to say, but at least half a wavelength, maybe more. The Yagi is a slow-wave structure, its capture area at the front is large, perhaps 1 wavelength square for a 10 dBi antenna. Halfway along the boom the sensitive region is smaller.
Use a non-conductive pole. I used many filament wound fiberglass poles for this purpose. Again, you probably want a half-wavelength clearance from the boom, but a third of a wavelength will work. The coax of course can't go in the tube, so it has to hang down from the very back, somewhat behind the director.
It is possible to put the coax in the pole if it's adequately loaded with ferrites. At 30 MHz I'd use a string of about 50 beads, 1.5" long, 1/2" dia, 1/4" hole, made of material 31, big enough for RG223 or RG58 to fit. You could also use three or four larger cores of 61 material, 1 m apart, wound with 6 turns of coax.
Finally, as you're only looking for a narrow band, you might be able to design some sort of quarter wave trap, several of them in series, on the coax or even on the metal pole. This would need to be carefully designed in simulation, and I've never tried it in this application.