No I mean, if people know I can use Bitpay, then they also know I am using a wallet that is compatible with BIP70 payment requests. As I refer above responses, I did not know some wallets could not support Bitpay. I know it is not a big problem, but now I am reading it up, it appears only 2 wallets are capable of receiving bitpay invoices, and yes, I'm using one of them. So now I know Bitpay knows I am a user of one of such wallets
I dislike already cookies that even tell websites what computer and OS I am using. So this upsets me a little bit. I had no idea Bitpay was like this.
No they don't necessarily. As posts above mentioned, you can still make a transaction to bitpay from a non-supportive BIP70 wallet, and Bitpay will have no clue from where the funds came from.
And even if they did knew that your transaction came from "one of such wallets", what use would that be? 95% of the bitcoin community uses Bitcoin Core / Electrum.
(Also, if you're using Electrum (I presume you do) like a "normal person" ( not looking at the Electrum server you connect to) you have more to worry about than Bitpay knowing what kind of wallet you use.)
Electrum works differently from a lot of other SPV clients. With Electrum, users are required to connect to Electrum servers. The way blockchain.info track the IP transactions is to see who relayed the transaction to them first. If you're using Electrum, the only possible IP address you would see there is the server's. This does not mean that your privacy is preserved; Electrum servers can see all the addresses in your wallet.