I managed to fix this with some help. Just in case somebody gets stuck see below updated code.

Added session rows to store current username in routes.py:

from flask import render_template, flash, redirect, url_for, request, session
from flask_login import login_user, logout_user, current_user, login_required
from werkzeug.urls import url_parse
from dashapp import application, db
from dashapp.forms import LoginForm
from dashapp.models import User
from dashapp import app1

@application.route('/')
@application.route('/home')
@login_required
def home():
    return render_template('home.html')

@application.route('/login', methods=['GET', 'POST'])
def login():
    if current_user.is_authenticated:
        session['username'] = current_user.username
        return redirect(url_for('home'))
    form = LoginForm()
    if form.validate_on_submit():
        session['username'] = form.username.data
        user = User.query.filter_by(username=form.username.data).first()
        if user is None or not user.check_password(form.password.data):
            flash('Invalid username or password')
            return redirect(url_for('login'))
        login_user(user, remember=form.remember_me.data)
        next_page = request.args.get('next')
        if not next_page or url_parse(next_page).netloc != '':
            next_page = url_for('home')
        return redirect(next_page)
    return render_template('login.html', form=form)

@application.route('/logout')
def logout():
    session.pop('username', None)
    logout_user()
    return redirect(url_for('login'))

And session in the callback for app1.py:

import dash
import dash_html_components as html
from dash.dependencies import Input, Output
from dashapp import application
from flask_login import login_required
from flask import session

app1 = dash.Dash(__name__, server = application, routes_pathname_prefix = '/app1/', assets_folder = 'static', assets_url_path = '/static')
app1.scripts.config.serve_locally = True
app1.css.config.serve_locally = True

app1.layout = html.Div(
    children = [
        html.Div(id='div2'),
        html.Div(id='div3', children = 'xxxx'),
    ],
)

@app1.callback(
    Output('div2', 'children'),
    [Input('div3', 'children')])
def update_intervalCurrentTime(children):
    return session.get('username', None)

for view_func in app1.server.view_functions:
    if view_func.startswith('/app1/'):
        app1.server.view_functions[view_func] = login_required(app1.server.view_functions[view_func])

Faced the same problem. I guess the problem is that current user hasn't been initialised when the 'application' registers Dash app. Nice workaround, though seems a bit insecure since Flask sessions are just encoded.

https://github.com/RafaelMiquelino/dash-flask-login/blob/master/app.py - more robust solution in my opinion. It checks current_user in the callbacks and uses contents of the page as Input, so the callbacks are called on page load. You can also skip the protection of the views if user experience isn't an issue.

Here's a simplified example of how I used it:

@app.callback(
    Output('graph-wrapper', 'children'),
    [Input('page-content', 'children')])
def load_graph(input1):
    if current_user.is_authenticated:
        return dcc.Graph() # Dash Graph populated with current_user data from db
    else:
        return ''