Plumbing – Is grout in the toilet a plumbing clog concern

There is a clog downstream from both of these drains. If they are both at the lowest level of the house and you have a septic system, then it's conceivable that the problem is there, but you'd also see water backing up into that bathroom when you run any other showers/toilets in the house.

Most likely, the clog is in the joint in the drain lines where the shower and toilet join on their way out of the bathroom. Get a snake to fish down the drain (probably best to do this in the shower to avoid damaging the toilet bowl) and expect to go down quite a few feet before you reach the problem.

Edit: Revisiting this question, I'd agree that there's also a likely vent blockage from the bubbling descriptions. But the fact that toilet water backs up into the shower points to a drain blockage, too, and that will be easier to fix.

The drain line is probably filled with hair and soap, chemical drain cleaners at best push the clog further down and make things worse in my opinion (now toilet backing up) with the exception of “mule kick” that will eat metal pipes and I am not sure if it is even available any longer. What you need is a real snake a small one to be run down the shower, and possibly a larger power one to be run down the toilet. Without cleaning the clog this will get worse this kind of snake you hold in one hand and spin pushing it down the drain a little at a time probably less than 2 or 3 chemical treatments. You should have the land lord take care of this incase any damaged pipe or other problems come up and you are not taking the $ hit for something that should be fixed by them.