Hell yes. For the plastics more than for the microwaves. I don't put anything hot in plastics if I can help it, and avoid cooking with them completely.
Oven vs microwave
ceramic vs plastic
you do realise microwaves are literally everywhere, and so are plastics
You do realize that just a few years ago, perhaps when your grandparents were born, that wasn't even remotely true?
Plastics and most other synthetic chemicals have been out in the public for less than a hundred years. Every year more chemicals are shown to have negative consequences on health. And a lot of time it's completely hidden by the companies involved.
Here's some reading material about these "safe chemicals" that are literally everywhere, for anyone who just wants to brush this aside:
Pentachlorophenal and napthalene (wood preservatives used in creosote)
Did the EPA Prosecute and Jail a Mississippi Lab Owner Because of Her Activism?
International Treaty Bans Pentachlorophenal, U.S. Continues Use on Utility Poles and Railroad Ties - eNews Park Forest
PFOA (chemical in teflon, waterproof clothing/furniture and many other products)
The Lawyer Who Became DuPont’s Worst Nightmare
DuPont’s deadly deceit: The decades-long cover-up behind the “world’s most slippery material”
Tris (fire retardant in furniture, children's toys, clothing, etc.)
Arlene Blum’s Crusade Against Toxic Couches
A Flame Retardant That Came With Its Own Threat to Health
Brominated fire retardants (replacement for Tris that turned out to also be bad)
New Studies Find Dangerous Levels Of Toxic Flame Retardants In Household Dust
Toxic effects of brominated flame retardants in man and in wildlife. - PubMed - NCBI
Hexavalent chromium (the Erin Brockovich chemical used in dyes, paints, and chrom plating)
The Dangers of Hexavalent Chromium (Chromium 6) in California Drinking Water
Health effects of Hexavalent Chromium
Phthalate plasticisers (in all sorts of plastics)
Phthalates are everywhere, and the health risks are worrying
How dangerous are phthalate plasticisers?
Bisphenol A (all sorts of plastic and metal food packaging)
The real story behind Bisphenol A
The Politics of Plastics: The making and unmaking of Bisphenol A "safety"
Carbon disulfide (created during the process of making cellophane, sausage casings, sponges, etc.)
Carbon disulfide poisoning and male hysteria
Carbon disulfide: Its toxicity and potential dangers
That's just a glimpse. There are over 60,000 new chemicals that have been created and placed in our products since just the 1930s, and most of them have never been tested by anyone other than the company that makes them for profit.
My advice is to expose yourself, especially your food, to as few things that don't exist in nature as possible. Use as few chemicals and plastics as possible, especially when heating things where chemicals can leach out. And avoid preservatives and other non-food ingredients as much as you can.