How can we charge our insurance premiums to our credit card without using apps like cardup?

Most insurance companies avoid taking in credit cards because they are try to avoid paying fees to the bank and the card issuer (visa/mastercard/amex). Just imagine the amount of premiums they receive every month and you can see why.

Not sure about others but AIA allows it for the first payment of new policies. After which they will ask you to pay via othe rmethods.

Depends on the specific insurance. AXA doesn't allow, while GE can only use the GE cashflow card. Prudential accepts any card.