Is it okay for a bank to turn away minors solely based on age even if they have a parent/guardian to sign/co-sign on the minor's behalf? Would it be considered age discrimination?
It is age discrimination, and it is legal. There is a federal prohibition against discriminating in employment provided that you are at least 40 years old. There are innumerable laws that require age discrimination w.r.t. being under 18, such as the lack of a right to vote. Contracts with minors, such as are involved with opening a bank account, are generally invalid with the exception of "necessities", education and insurance in Massachusetts. No law compels a bank to "accept" any person (to open a saving or checking account – even more so with accepting a loan application). A bank account would be a "public accommodation", which is not subject to a "no age discrimination" requirement at the federal or Massachusetts level.
To make a bank account you need to sign a contract. To sign a valid contract, a person needs to have the legal capacity to sign contracts. Minors are not able to sign most contracts. This is not illegal age discrimination under federal laws, it is a law for the protection of minors!
Unless the minor is emancipated or the bank account is a necessity, the contract would be void ab initio and neither could the minor demand it's enforcement nor could the bank demand its payments. But if the bank account is a necessity (it likely is), then a 16-year-old is allowed to sign and could open a bank account on its own.
There is special law for accounts of minors:
Massachusetts state law requires state-chartered banks to provide no cost checking and savings accounts to anyone 18 years old or younger or anyone 65 years old and older. Some federally chartered banks also have special accounts that may offer reduced or limited fees.
And the government even has more helpful information about those:
Credit unions and federally-chartered banks are not required to offer such accounts.
Those under 18 may be required to have a co-signer in order to open an account. Married couples cannot be denied opening an account as long as one spouse meets the age requirements.
A full listing of all Massachusetts state chartered savings banks, co-operatives banks and trust companies subject to the 18-65 law are available at the Division of Banks website.
So, the Massachusetts law does dictate that some banks have to provide a no-cost savings/checking account to minors. However, the bank might require someone to co-sign for ages 16-18, and has to do so for minors under 16, in which case the guardian would need to open the account in the name of the child.
Generally, I suggest to take the minor and their guardian and meet at one of the banks that offer such an account and discuss with a bank employee the account.