If Romeo and Juliet was set in 2019, would it have the same ending in regards to cultural traditions?

This is a complex question. The play seems clearly set within the cultural and marriage conventions of fifteenth-century Italy or sixteenth-century England. However, it has been restaged in any number of ways since it opened in the 1590s. Some stagings that try to stay true to the original time period are highly effective, suggesting that the play still speaks to later audiences. Updates to current times work equally well. All end with the young lovers' suicides.
One of the challenges with asking the question this way is that it assumes that cultural traditions are a monolith, yet in 2019 we see incredible diversity. We may be less likely to see a family feud like the Capulets and Montagues maintain, but we certainly do see religious and ethnic divisions. In many ethnicities, marrying outside a faith or community would still be transgressive, engendering the type of control Juliet's father seeks to impose on her. Certainly within the LGBTQ community, a young person's family can exert this same control, insisting that a child love differently. Because the Capulets are focused on status-climbing by means of Juliet's marriage, parental expectations of what a child's adult life should signify remains relevant within the play.
Suicide is high among young people and especially LGBTQ adolescents, often because of the insistence that the person live a life of deceit regarding love and marriage. Because people at this stage of life often think in extremes or absolutes, weathering the compromises older people want to impose on them can seem devastating. We can see Juliet's decision to kill herself as a rejection of a world not just without Romeo in it but also one in which the crude and abusive toxic masculinity of the first three Acts is untenable. By the time Juliet first fakes her death and then actually kills herself, she has seen every adult in her world let her down or ask her to compromise her integrity as well as her love for Romeo.
The fact that the lovers' fathers engage in a silly competition (feud) over who will erect the best monument to the other's child suggests that this world is not capable of learning from the tragic events. Juliet seems to intuit that intransigence of spirit when she makes her choices in act 5.
Shakespeare typically writes universal stories but with a keen understanding of specific psychology that transcends time and place. Capulet and Montague are not necessarily typical of their time, though they are tolerated by it. The Prince and others comment on the disruptiveness of the feud but see it as an annoyance more than an outrage. As a result, they allow the violence and tribalism to increase and become so absolute that Romeo and Juliet lack agency in pursuing their affections. Friar Lawrence uses these young people to try to resolve the animosity between the fathers, but in doing so he suggests also that Romeo and Juliet are merely pawns to others' social goals. He lacks courage to counsel his parishioners on his religion's law of love and acceptance, preferring to work in tricks and secrets.
The play speaks finally to Verona's culpability in allowing these approaches to violent and divisive behaviors. As we see an increasing number of street protests or virulent rejection of others' rights to hold the views they do, we have seen an uptick in families saying they would prefer a child to marry outside their race or ethnicity rather than to marry outside the family's political views. The universal impulse to define oneself against other groups, therefore, is a cultural tradition as common today as it would have been in Verona. And that impulse often leads to tragedy.
A few slight tweaks to the play seem to suggest, then, that without a change of heart and mind, the ending of this play is as inevitable now as it was originally.