ConsenSys/smart-contract-best-practices

@MicuEmerson

pragma solidity ^0.5.2;

contract Test {
    bool public access;
    address public owner;
    string public _firstName = "";

    constructor() public  {
        owner = msg.sender;
    }
   modifier checkAccess(bool _access) {
        require(
            access == _access, 
            "Access denied"
        );
        _;
    }

    function getAccess() public returns (bool success){
        if(msg.sender == owner){
            access = true;
        }
        else{
            access = false;
        }
    }

    function getFirstName() public checkAccess(this.getAccess()) returns (string memory firstName){
        return (_firstName);
    }

    function setFirstName(string memory name) public {
        _firstName = name;
    }

}

Since in your case you are using public view getAccess and view functions do not modify the state, thus even if you were getting true for that instance, however it was not persisted in the state, thus, you were getting a transaction revert.
I have tested above code on Remix compiler and it works as expected.