Hi,

Try to use right property instead of dropdown-menu-right :

import React, { Component } from 'react';
import {
  MDBNavbar,
  MDBNavbarBrand,
  MDBNavbarToggler,
  MDBCollapse,
  MDBNavbarNav,
  MDBNavItem,
  MDBDropdown,
  MDBDropdownToggle,
  MDBIcon,
  MDBDropdownMenu,
  MDBDropdownItem
} from 'mdbreact';

class InputPage extends Component {
  state = {
    isOpen: false
  };

  render() {
    return (
      <MDBNavbar color='elegant-color-dark' dark expand='md'>
        <MDBNavbarBrand>
          <div className='logo-wrapper 20x20'>
            <a href='#!'>
              <img
                style={{ width: '60px', height: '60px' }}
                alt='Arrg Logo'
                src='https://i.imgur.com/sEitLk6.png'
              />
            </a>
          </div>
        </MDBNavbarBrand>
        <MDBNavbarToggler onClick={this.toggleCollapse} />
        <MDBCollapse id='navbarCollapse3' isOpen={this.state.isOpen} navbar>
          <MDBNavbarNav right center>
            <MDBNavItem>
              <MDBDropdown dropdown-menu-right>
                <MDBDropdownToggle nav caret>
                  <MDBIcon
                    icon='user'
                    height='60px'
                    width='60px'
                    className='center'
                  />
                </MDBDropdownToggle>
                <MDBDropdownMenu right className='dropdown-dark'>
                  <MDBDropdownItem href='/'>Home</MDBDropdownItem>
                  <MDBDropdownItem href='/create'>
                    Create your Arrg-ument
                  </MDBDropdownItem>
                  <MDBDropdownItem href='/profile'>
                    View your Profile
                  </MDBDropdownItem>
                  <MDBDropdownItem onClick={this.onLogoutClick} href='/'>
                    Logout
                  </MDBDropdownItem>
                </MDBDropdownMenu>
              </MDBDropdown>
            </MDBNavItem>
          </MDBNavbarNav>
        </MDBCollapse>
      </MDBNavbar>
    );
  }
}

export default InputPage;

Hope I could help.

Best regards.