Leading by Example.
Usually, I'm the GM at the table, but sometimes I'm a player, most often at conventions when I don't organise or am invited as a local GM.
I try to lead by showcasing my enjoyment of roleplaying. Sometimes this works other times it doesn't. It tends to work at tables that are laid-back, and at tables that have young enthusiastic players who are eager to learn and who are easily affected by my positive attitude.
I try to show that you can find solutions to problems by roleplaying instead of purely utilising mechanics and if it is in-line with that GM's table, then they allow for that kind of play. They will see that roleplay is rewarded and that often is enough motivation for them to also seek that reward by roleplaying.
Talk about how much fun you have with your roleplay during breaks and finally respect that if there aren't interested in a lot of roleplay that it is a two-fold choice.
First, it is their choice and agency, and second, it is the table's obligation to set the framework. You are one player of that table, and you can address issues and encourage to have a new (or first) Session 0.
Establish a framework in a Session 0.
A framework will establish what kind of game you want to play. It will set guidelines, expectations, atmosphere and mood. You want to be on the same page with your group, and you care for roleplaying. Grab the initiative to pursue your goals, and confirm whether they are common goals for your table.
If you are the one who initiates the topic, then you will set the initial tone. So show your friends that you want to be on the same page to get a better experience overall. View my link that is meant for your GM and see the checklist about what to discuss during a Session 0.
If you have a framework that out-rules jokes about sensitive topics, then your table can evict a player that breaches that contract. During my years as a GM, I have done that (evicted a player for egregious conduct) 4 times with a 100% success rate in improving the game for all other players at the table. My decision was always discussed with the whole table, including the offensive player and backed up by all other players for which I was the spokesperson as a first among equals because I moderate the discussions in my role as GM (not DM).
Some people are blissfully unaware of their social incompetence because they assume that some behaviour is normal and when you make them aware they will adjust, most of the time.
Ordinarily, it is enough to state that the conduct is a problem, point out why the conduct is a problem and how they can enjoy what they do without offending you. When you do that, don't initially accuse them of doing something wrong, instead explain how it is affecting you and why you perceive it as wrong (I have not once observed that the "you are wrong" approach solves an issue at any table).
For instance, establish in your Session 0 that rape, yes that includes jokes, is off-topic at the table or else you won't be able to enjoy your time at the table. Hold people accountable for breaching Session 0 contract, warn them and if they don't take the hint, evict them together as a table of players. If the table doesn't establish that rape is off-topic and that is a dealbreaker for you, then don't compromise, there are other tables. Try to discover your dealbreakers and when you are willing to compromise. I'm using the topic of rape as an example of a sensitive topic that is divisive for many tables (and is often carelessly joked about).
For the phone player at your table, it is the same process - is it a dealbreaker or is there are a compromise? Please read this perspective and solutions for players who are constantly on their phone.
Collaborate among equals.
Always remember that you are a table of equals and in some situations, the GM (DM rules in 5e; organisation in general) or an offended player (more harm done than joy gained by jokes) is the first among equals.
You have a DM/GM who is shy and not assertive, so they could use some help in preparing a Session 0 that may solve your issues, read how I GM a Session 0 and encourage and help them to organise the Session 0.
You can initiate the action to foster change at your table by talking to your group of players and your DM. You can set the course that will arrange the Session 0 in which you, the other players and your DM will work together to create a solution. As the one who initiates the action, you set the tone.
As a player, I have had success with arranging and helping the GM at a convention table by making him aware that some topics where uncomfortable for one of my fellow players which also affected my own enjoyment by association. He constantly made jokes about the size of the breasts of the assistant of the big bad evil wizard, and generally spent a lot of time sexualising her. I was annoyed by his insensitive behaviour, while the other player was visibly uncomfortable. So I asked to prepone the next short break and addressed that his behaviour made us feel uncomfortable and that we didn't exactly feel respected by his descriptions. He was embarrassed and toned down his language, making it less sexual, less objectifying while keeping his scene intact (she was still a beautiful woman who dressed confidently, but her breasts were no longer almost popping out of her corset and her glistening sweat pearls running down all places of her body no longer mattered as much).