1. Brokers such as eToro trade in more than crypto e.g. stocks, currencies. So if I transferred money directly from my bank to a company such as eToro which isn't exclusively crypto, is this likely to be flagged as a banned company from my banks perspective,
The reason why you are not banned from using this service is that they do not own Bitcoin or rather they do not sell you bitcoin, you get something that has the same value of bitcoin and when you want to withdraw, you are withdrawing your profits in USD and not the bitcoin.
in short, Not your keys, not your coins. Avoid it if you want to keep BTC for long time.
2. To avoid this, am I better to use something like PayPal for my crypto transactions?
PayPal does the same, you cannot withdraw Bitcoin
If you give us more information such as your country, or the payment methods that you can obtain, we can give you the best method for you.
Some people buy gift cards for cash and sell them for Bitcoin which are anonymous and good for small amounts.