You need to be cautious with a post-exchange, cash-out mortgage.
However, typically the issue arises when the relinquished property is mortgaged during the exchange period unless there is a business purpose for refinancing.
Mortgaging replacement property post-exchange is typically not problematic, but caution and guidance would still be recommended.
See https://www.americanbar.org/groups/real_property_trust_estate/resources/real_estate_index/section-10...
See also https://www.accruit.com/blog/cash-out-refinance-or-after-1031-exchange
