Googling "1-methyl 3'-pseudouridine" brings up 14 hits not all actually containing the term and some on facebook. I think this refers to N1-methylpseudouridine.
From a EU report on Moderna's vaccine:
The RNA contains modified N1-methylpseudouridine instead of uridine to minimise the indiscriminate recognition of the mRNA by pathogen-associated molecular pattern receptors (e.g. TLRs
There's a paper that also suggests that's in Pfizers vaccine.
Googling it + FDA doesn't show any discussion that you would likely see if it's the reason that the FDA rejected other approval.
The fact that the substance naturally occurs in mammal also suggests that it's not toxic and mammals can handle it generally.
I think you are indeed making a mistake by letting unsourced FB claims worry you, given the known proliferation of antivax-driven misinformation. There is an extremely low probability that you're first hearing about a real issue via some random, unsourced FB comment.
For more evidence, look to the overreactions to J&J / AZ adverse effects. Regulatory bodies are clearly willing to make a public fuss over even small probabilities of things going wrong.
What are the modified RNA bases in mRNA Covid vaccines and/or how are the metabolised in the human body ? Have you heard about any safety issues with these modified bases ?
For Pfizer, I know, that the modified bases are 1-methyl 3'-pseudouridine. From there, wikipedia directs me to the page on pseudouridine, which is naturally present in tRNA. However, it is not the same chemical. I do not know how easy or difficult for the human body is to remove the methyl moiety.
For Moderna, I do not know what are the modifications at all.
The reason I am worried: I have seen an unsourced claim on facebook, that Moderna has had a problem getting approved several of their products, because of the toxicity of the modified bases. Maybe it is a failure mode, letting an unsourced claim start a process of worrying and searching the information on the modified bases. But the process has already started in my head... I would very much appreciate some details, if you guys know them. (Apart from the obvious info, that the clinical trials did not show any short od medium- term problem).