You can bridge through JavaScript. It's not a big deal in practice. WASM is still very immature. You do not want to build your whole app in WASM if you want to keep a full head of hair.
It does limit a lot of use-cases from being viable in WASM.
Anything that needs to do a lot of DOM access will probably see a big performance hit if you rewrite it in WASM because there will be too much overhead from crossing the JS-WASM border.