I think the other answers are correct in that both of these are factors:
- Trump and some of the Republican leadership (repeatedly) slamming postal voting
- Republicans being less afraid of Covid-19 and thus less inclined to socially distance (also reflected in some of Trump's comments on the pandemic and his personal example)
Alas answers (and comments) have mostly posited one or the other (of the above two) as being the main factor (and even downvoted answers that suggested the other one), but without any data to support which was the main contributor.
It's probably difficult to ascertain the separate contribution of these factors. It's much easier to notice the trend over time though in the divergence of Democrat and Republican opinions on mail-in voting in 2020, e.g. from a UCSD/Lucid series of surveys:
We find a significant, growing gap over how citizens want to cast a ballot. In April, 40 percent of Democrats said they would like to vote by mail, while 30 percent of Republicans indicated the same. By June, that gap had grown to 20 percentage points, with 45 percent of Democrats saying they’d vote by mail to 25 percent of Republicans. By August, half of all Democrats said they want to vote by mail this election, while only a quarter of Republicans said they would, for a gap of 25 percentage points.
We saw the same pattern in how respondents want others to vote. When asked in April whether they support sending mail ballots to any voter who requests one, 87 percent of Democrats and 64 percent of Republicans agreed, for a gap of 23 percentage points. By August, this gap grew to 33 percentage points. Over 80 percent of Democrats supported this policy, while Republicans were essentially evenly divided between supporting and opposing absentee voting by request, which is in place in most states, including nearly every swing state in the presidential election.
Why do so many more Democrats than Republicans plan to vote by mail?
One clear explanation of the growing gap has been well documented: Partisans often take cues from their party’s elites, as scholarship has long found. When Trump criticizes voting by mail, as he frequently does, Republicans take note. When other Republican politicians reiterate Trump’s comments, the cue is made even more clear.
But we found another possible reason: Republicans and Democrats respond differently to information about the pandemic. When we showed respondents projections about how the pandemic would probably unfold, Democrats became more likely to want to vote by mail. Republicans did not.
Reading the projections had the biggest effect in April. As both the pandemic and the election campaigns unfolded, covid-19 projections mattered less. At the same time, the differences in Democrats’ and Republicans’ plans grew. This suggests that Americans’ opinions crystallized somewhat over the summer as those two groups’ views of the pandemic diverged.
(Besides the WaPo article in which those academics popularized their findings, they've also published PNAS paper on the topic.)
Alas, while it's thus fairly easy to establish both as (probable) causative factors, even that research did not attempt to quantify the relative weight of each factor, which may actually be no easy task...
(An interesting aside to note is that back in April, many more Republicans than Democrats said the election was going to be conducted fairly.
Fewer than half of Democrats (46%) were even somewhat confident in an accurate and fair election, compared with 75% of Republicans. And Democrats were deeply concerned over whether all citizens would be able to vote: Just 43% of Democrats said they were very or somewhat confident all citizens who want to vote would be able to do so, while about twice as many Republicans (87%) were confident all citizens would be able to vote if they wanted to.
The expansion of (no excuse) mail-in voting in response to Covid-19 seems to have been negatively correlated with that relative split of opinions on the matter between Republicans and Democrats. Or at least this much was clear from another April survey:
According to an NBC/Wall Street Journal poll conducted in April, over half (58%) of Americans are in favor of permanently changing laws to allow everyone to vote by mail. However, there is a very large partisan divide with only 31 percent of Republicans agreeing, compared to 82 percent of Democrats.
Perhaps more relevant to the "why" question at hand though:
A Pew Research study conducted in June also found similar results when they looked at support for so-called “no excuse” early voting, or voting early without requiring a documented reason. [...] The Pew poll found that among Democrats and Democratic-leaning independents, an overwhelming majority (83%) support no excuse early voting compared to only 44 percent of Republicans and Republican-leaners. Furthermore, among the remaining 55 percent of Republicans who think a documented reason should be required to vote early, 37 percent say the COVID-19 pandemic should not be considered a valid reason, while only 17 percent think it should be a considered a valid reason.
These differences go to the very core of what people think maintains the security of elections. Nearly eight in ten Democrats (79%) believe that changing election rules to make absentee ballot voting more available would make it easier to vote and would not jeopardize the security of the elections. A majority of Republicans (59%) disagreed, saying that making voting easier would have an effect on election security.
This partisan framing of this issue is a recent occurrence. This year, polls showed that over half (62%) of Democrats planned to vote early, while only 28 percent of Republicans planned the same. Historically, this partisan difference has been no more than about two percentage points. Additionally, in the past, differences in opinions on this topic were driven mostly by geographic location rather than party affiliation, with people who live in the western states being much more likely to vote by mail.
Alas the way that last survey was structured doesn't allow definitive conclusions (either) on the "why did Republicans oppose", but there's clearly some overlap in factors: Covid-19 not being seen as a valid excuse (on one hand) and the broader (Republican) view that mail-in voting would worsen security (on the other hand).