This is from a recent study published in Science Advances:
The participatory and partisan impacts of mandatory vote-by-mail
Quote:
"Using a unique pairing of historical county-level data that covers the past three decades and more than 40 million voting records from the two states that have conducted a staggered rollout of mandatory vote-by-mail (Washington and Utah), we use several methods for causal inference to show that mandatory vote-by-mail slightly increases voter turnout but has no effect on election outcomes at various levels of government."
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It appears then that neither party should have a real cause for concern. The net benefit is positive; a slight increase in voter turnout.