We figured however we put it into the cabinets, those holes are easier to fill than tile holes. I don't mean to be adversarial, but I disagree completely. Replacing a tile is a 15 minute and $15 DIY job, getting a paint and sheen match on cabinets is something I would not even try and I have years of experience doing it. I would just respray the entire sides of your cabinet as that would take 1/10th the time of trying to match them. However, the problem isn't drilling through your tile and that wouldn't work either. You need to accomplish what you want without drilling through the sides of your cabinets. Which can easily be done. You can make it look like it was a planned part of the kitchen and not an afterthought while preserving the sides of your cabinets. Or something like this..

I pushed the glass to the side a little bit and it revealed a screw between the frame and the glass. It appears the glass may be held in place by 4 rectangular pieces. Two on each side. I’ve attached pictures.

We did ours like this, with a similar corner (though it looks like you have a little more space between the sink and the stove wall, so might want to wrap the corner). These shelves are 18.5" off the counter, which was intended to allow for uppers to go there in the future (though we are now 12 years post-reno and haven't done that yet, so may never get to it!) One thing I would do differently is the tile behind the range--it was supposed to meet the hood but for reasons I can't remember anymore, the spacing was off so the tile extends slightly beyond the hood and we had to end it short to avoid it looking really odd. The hanging utensils bar was a fix when it still looked strange. There were also supposed to be two shelves on the right side, but we realized all the bottles we wanted to keep there would hit the top shelf, so decided to put the second in another area of the kitchen instead. In general, we planned these based on what we wanted to store on them (and mapped out the whole kitchen for that at the time we renovated). If you plan to do a gut remodel at some point in the future, it probably doesn't matter as much how far up you tile or where exactly you place the shelves as long as it works for you now. Our shelves and tile were also all DIY, so if you have a contractor they can probably get more creative on solutions and placement. (We were not up for opening our plaster walls, for instance, even though that would have been the way to get the ideal placement of the shelves since you could then place blocks.) Also yes to a good range hood (and know that even with that, you will get some grease on items on the shelves--though it's been much better than I expected, and we really only have issues with it on the oil shelf where items are right up against the range). The primary issue on the long shelves is just dust, but we definitely expected that and give it a good clean a couple times a year, which seems to address it enough for our needs. YMMV based on your tolerance for that!

Just make sure you pick up at least two studs. Use 2" screws. Friction alone will keep shelf onto the rods. Don't use adhesive. If you ever want to move or remove that shelf you'll be demoing that wall. Source: Burbon Moth Woodworking youtube video