As far as a modified sine wave inverter, I would just say NO! The pure sine wave inverters are so cheap now that it is not so painful to throw out the MSW and replace with Pure sine wave.
I would never even own a MSW nowdays given the potential for device damage.
Some transformers will be fine, some can get hurt. Transformer being the "brick", or big thing you plug into the wall to charge your phone or other item, or to power an electronic item. keep in mind that most electronics actually run off of DC power, not AC power, they have built in AC to DC transformers.
Light bulbs, motors, fans, heaters, vacuum cleaner (basically a fan) are all AC, but
TVs, radios, phones, computers, music amps, most all electronics that use chips... all run off of DC power (provided by an AC to DC transformer).
Also fwiw, even the cheapest of cheap PSW inverters give a very clean, very neat sine wave. I checked with an oscilloscope. It is better than your house, way more clean therefore safer.