Is 1½ hours enough for a transit at Munich Airport?

Presuming you are arriving from a non-Schengen country then you will not need to pass through immigration in Munich. You will remain air-side, although you may need to go through security depending on which terminal you arrive in/depart from.

However even if you do need to clear immigration in Munich you'll find it very quick and easy (presuming you come from a country that does not require a Visa) - I don't recall ever having to wait more than a minute or two when passing through immigration in either Munich or Frankfurt. Security can be another story and can take a while to get through depending on how busy they are, but 90 minutes should be plenty of time as long as your inbound flight is on time or only slightly delayed.

It is interesting to me how different it is to transit in Munich and in Frankfurt. I have had 60 minute transits in Frankfurt that I made only by butting to the beginning of lines (showing people my boarding pass and begging them to let me go first) and running, and not getting to go to the bathroom or buy a drink, and still only just making the flight. But a 60 minute transit in Munich? I have done it many times (always a Schengen/non-Schengen transfer - Canada or the UK into Schengen, or Schengen headed out, so in addition to security there are passport lineups to deal with) and always seem to end up with 20 minutes to sit at the gate and drink the free coffee.

Munich is smaller than Frankfurt, I find the signage simpler to follow, and it's just less disorienting and crowded. The lines are shorter and perhaps the overall volume of passengers is less. Whatever the reason, I just don't transit through Frankfurt any more and I'm always happy to do so through Munich. A one-hour connection in Munich doesn't worry me, so I wouldn't be worried about your 90 minute one.

One disclaimer: this is if your flights are booked as a single ticket. If your incoming flight is significantly delayed you will misconnect. If your flights are booked as one ticket this is the airlines's problem and they'll take care of you. But if they are booked as separate tickets then you're just out of luck. In that case I would want a much longer connection (3 hours or more) to feel safe.

Necromancing, in case anybody else has this problem.
I actually did this with a flight to and from Romania.

Both times, it was very tight.
Baggage was changed automatically.
But because I didn't have a biometric ID card, I had to stand in line for manual passport control, which took long time, because there were many people and ony one or two manual control points open.

It will be very tight, but it will work.
The problem is, Munich airport is quite large.
You'll drive around the airport quite long when you arrive, and then have to go through passport control.
With 1.5 hours in between flights, you will board about 5 minutes before boarding time ends.

But if your flight arrives late, you'll need to make yourself noticed and use the express lanes.