Looks to me like minmax(min-content, 1fr) or fit-content(1fr) are actually not supported.
Does this approach fit your use case?
.my-grid {
display: grid;
grid-auto-columns: 1fr;
grid-auto-flow: column;
column-gap: 1rem;
row-gap: 1rem;
}
.my-item {
min-width: min-content;
white-space: nowrap;
}
<div class="my-grid">
<div class="my-item">Some potentially pretty long text...</div>
<div class="my-item">Some other text</div>
</div>