Wifi issues with ESP8266 (Wemos D1Mini) when OLED via I2C is connected

I have an Issue with my Config. If I start my small climate sensor package with an OLED connected, the ESP will start but won’t post any data to Homeassistant. If I disconnect my OLED and restart the ESP everything is fine. This is my first real project with ESPs so there may be a big rookie mistake somewhere.
Is there a possible solution with delays for sensors or the I2C bus?

This is my config:

sensor:
  - platform: bmp085
    temperature:
      name: "Raum Temperatur"
      id: bmptemp
    pressure:
      name: "Raum Luftdruck"
      id: bmppressure
    update_interval: 60s



  - platform: dht
    pin: GPIO00
    temperature:
      name: "Raumtemperatur DHT22"
      id: dhttemp
    humidity:
      name: "Luftfeuchtigkeit DHT22"
      id: dhthumid
    model: DHT22
    update_interval: 60s

binary_sensor:
  - platform: gpio
    filters:
      - delayed_off: 3s
    pin: GPIO16
    name: "Screen button"
    id: screenButton

display:
  - platform: ssd1306_i2c
    model: "SSD1306 128x64"
    update_interval: 1.0s
    address: 0x3C
    lambda: |-
      if (id(screenButton).state){
        it.printf(0, 10, id(roboto_light), TextAlign::LEFT, "Temperatur: %.1f°C", id(bmptemp).state);
        it.printf(0, 30, id(roboto_light), TextAlign::LEFT, "Luftdruck: %.fhPa", id(bmppressure).state);
        it.printf(0, 50, id(roboto_light), TextAlign::LEFT, "Luftfeuchtigkeit: %.f%%", id(dhthumid).state);
      } 

i2c:
  sda: GPIO04
  scl: GPIO05
  scan: False

font:
  - file: "Roboto-Light.ttf"
    id: roboto_light
    size: 12

Add

frequency: 800kHz

to the i2c part of the yaml, and you can also increase the update interval for the display to a higher value, because you set the interval for the dht and bmp sensor to 60 seconds, so why updating the oled every second if the displayed values changes once per minute?

display:
  - platform: ssd1306_i2c
    model: "SSD1306 128x64"
    update_interval: 1s
    address: 0x3C
    lambda: |-
      if (id(screenButton).state){
        it.printf(0, 10, id(roboto_light), TextAlign::LEFT, "Temperatur: %.1f°C", id(bmptemp).state);
        it.printf(0, 30, id(roboto_light), TextAlign::LEFT, "Luftdruck: %.fhPa", id(bmppressure).state);
        it.printf(0, 50, id(roboto_light), TextAlign::LEFT, "Luftfeuchtigkeit: %.f%%", id(dhthumid).state);
      } 

i2c:
  sda: GPIO04
  scl: GPIO05
  scan: False
  frequency: 800kHz

That was indeed helpfull. Thank you @jsuanet !