Partial issues with metamask while running tests with "chromeWebSecurity: false"

[drptbl]

It seems that metamask doesn't work well with Synpress if it's run with "chromeWebSecurity": false flag.
There seems to be some issues with connection between metamask and browser in this case.

In case of 1inch, I wasn't able to connect my wallet:

In case of kwenta, I was able to connect my wallet, but dapp couldn't read any balances from it.

Everything works fine with "chromeWebSecurity": true.
https://docs.cypress.io/guides/guides/web-security.html

Couldn't find anything helpful in this topic, only issues without answers, like this one:
MetaMask/metamask-extension#6817