Yeah, they can just deliver an alternate version of the web client (assuming the target user uses the web interface) -- probably the easiest (or least-detectable) way for ProtonMail to read a user's encrypted email contents.
https://dwheeler.com/trusting-trust/
There are also a number of people making minimal OSes, interpreters, and compilers that you can, for example, assemble by hand and type in "from scratch".
There was a nice list of those that I can't find right now, but you could look at
https://bootstrappable.org/projects/mes.html
as one example in this direction.
To make a perfectly secure system, the first step is to obtain high purity sand.
On the bright side, it's hard to imagine that many of these attacks will be self-propagating, which is the particularly insidious thing about the Trusting Trust attack. Yes, hardware is used to design hardware, but typically in a more indirect and heterogeneous way than the "compiler compiling itself" scenario. To be concrete, I'd say Microsoft or Canonical has much more to fear from a Trusting Trust sort of attack than Intel does, but the software developers also have better options to contain or detect such an attack.